library(readr)
library(HSAUR2)
## Loading required package: tools
library(SciViews)
library(scatterplot3d)
library(car)
## Loading required package: carData
library(lattice)
library(GGally)
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## method from
## +.gg ggplot2
library(ggplot2)
library(ggridges)
library(ggvis)
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## Attaching package: 'ggvis'
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library(ggthemes)
library(cowplot)
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## Attaching package: 'cowplot'
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## theme_map
library(gapminder)
library(gganimate)
## No renderer backend detected. gganimate will default to writing frames to separate files
## Consider installing:
## - the `gifski` package for gif output
## - the `av` package for video output
## and restarting the R session
##
## Attaching package: 'gganimate'
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## view_static
library(dplyr)
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## Attaching package: 'dplyr'
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## recode
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library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ lubridate 1.9.3 ✔ tibble 3.2.1
## ✔ purrr 1.0.2 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(grid)
library(gridExtra)
##
## Attaching package: 'gridExtra'
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library(RColorBrewer)
library(Hotelling)
## Loading required package: corpcor
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library(stats)
library(biotools)
## Loading required package: MASS
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## Attaching package: 'MASS'
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## select
##
## ---
## biotools version 4.2
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(FactoMineR)
library(ggfortify)
library(psych)
##
## Attaching package: 'psych'
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## %+%, alpha
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library(corrplot)
## corrplot 0.92 loaded
library(devtools)
## Loading required package: usethis
library(cluster)
library(magrittr)
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## extract
library(NbClust)
library(MASS)
library(leaps)
heart <- read.csv("/Users/pallemkrishnaniveditha/Downloads/heart_statlog.csv")
attach(heart)
str(heart)
## 'data.frame': 1190 obs. of 12 variables:
## $ age : int 40 49 37 48 54 39 45 54 37 48 ...
## $ sex : int 1 0 1 0 1 1 0 1 1 0 ...
## $ chest.pain.type : int 2 3 2 4 3 3 2 2 4 2 ...
## $ resting.bp.s : int 140 160 130 138 150 120 130 110 140 120 ...
## $ cholesterol : int 289 180 283 214 195 339 237 208 207 284 ...
## $ fasting.blood.sugar: int 0 0 0 0 0 0 0 0 0 0 ...
## $ resting.ecg : int 0 0 1 0 0 0 0 0 0 0 ...
## $ max.heart.rate : int 172 156 98 108 122 170 170 142 130 120 ...
## $ exercise.angina : int 0 0 0 1 0 0 0 0 1 0 ...
## $ oldpeak : num 0 1 0 1.5 0 0 0 0 1.5 0 ...
## $ ST.slope : int 1 2 1 2 1 1 1 1 2 1 ...
## $ target : int 0 1 0 1 0 0 0 0 1 0 ...
Inference: * This dataset comprises various medical attributes aimed at studying heart disease risk factors. It includes age, sex, types of chest pain, resting blood pressure, cholesterol levels, fasting blood sugar, results of resting electrocardiograms, maximum heart rate, presence of exercise-induced angina, ST depression during exercise, and the slope of exercise ST segment. * Each of these factors is used to understand their correlation with the presence or absence of heart disease, indicated by the “Target” column, where “1” suggests the presence and “0” the absence of heart disease.
stars(heart)
# Standardizing the data with scale()
matstd.data <- scale(heart)
# Creating a (Euclidean) distance matrix of the standardized data
dist.data <- dist(matstd.data, method="euclidean")
colnames(dist.data) <- rownames(dist.data)
dist.data
## 1 2 3 4 5 6
## 2 4.2286110
## 3 3.1831540 5.1041072
## 4 5.5226745 3.2651669 5.1408050
## 5 2.8940473 3.9317790 2.9301390 4.5459742
## 6 1.6089723 4.6607357 3.3273130 5.3665195 3.2849391
## 7 2.5278860 3.4857018 3.9695400 4.8608591 3.5358582 2.8984388
## 8 2.6316206 4.7217097 3.0537888 5.2376970 2.5525237 2.6231004
## 9 4.5657629 3.8785143 4.5968761 2.7714481 4.2025273 4.3971438
## 10 3.4074500 4.0593612 3.0464511 4.3633055 3.2460244 3.4264272
## 11 3.0091246 3.4995105 3.3881139 4.1593409 3.2655802 2.9458861
## 12 5.3910069 4.5504081 4.5621646 3.6281157 4.2924337 5.6881822
## 13 1.7374891 4.5108969 2.3793565 5.1881917 2.6831934 1.9683349
## 14 4.3718492 3.5713231 4.7460183 2.7177109 3.7577476 4.2041332
## 15 3.5175130 4.0086749 3.2363862 4.3062734 3.5362003 3.2096029
## 16 3.7843178 3.3597348 4.3827112 4.1484312 3.9667207 3.8573311
## 17 3.8565627 4.0618754 4.6495216 4.5076895 4.2981700 3.1868821
## 18 2.7668963 3.7421244 3.8877419 4.8613218 3.6843103 2.9588111
## 19 4.9976585 4.5451607 4.8350644 4.0548096 4.0976192 4.3381179
## 20 3.9944731 4.1837340 4.6771358 4.8225671 4.9548677 4.0277098
## 21 3.6513585 4.8654413 3.7952262 5.4260876 4.4262409 3.7403894
## 22 2.7116349 4.0027187 3.1036735 4.6419439 3.0180698 2.9152414
## 23 2.8414994 3.5588403 3.9942233 4.7755111 3.4181193 3.1269863
## 24 4.4443304 4.0065899 5.0744243 3.9834156 4.7811121 4.8468834
## 25 1.9356543 4.1579787 2.3392912 4.6684764 1.9635640 1.8371784
## 26 1.5163282 4.3013970 3.5826444 5.3715434 3.1177372 1.4630171
## 27 5.3581391 5.2182932 4.7405655 3.7245647 4.4228808 5.0041104
## 28 2.7037823 4.7261401 2.1909028 4.9691960 2.1564690 2.7421141
## 29 3.9817726 4.9767465 3.9061479 5.1327393 4.2467378 3.6773261
## 30 2.0395535 4.2533314 2.8110668 5.0687090 1.9786264 2.4571516
## 31 4.2008294 4.4023896 4.4370519 4.7913798 4.1254867 4.0442169
## 32 3.3129277 4.3625910 2.8785835 4.5477958 1.1856095 3.3598469
## 33 4.6699453 3.6618260 4.5354785 3.3442539 3.6275864 4.3235007
## 34 4.5078977 3.6458232 4.1960117 3.5979774 3.9762223 4.2492293
## 35 2.7326652 3.0659888 3.7665398 4.6280417 3.1055078 3.4929970
## 36 1.4001980 4.6569306 2.5982774 5.4673646 3.2453807 1.6805502
## 37 6.4492317 5.4789826 5.8427748 4.0376623 4.9659976 6.2844337
## 38 3.3268971 4.3498004 3.1601595 4.8461479 3.9474325 3.2122065
## 39 4.1025868 4.5614939 4.2544668 5.3106207 4.2545995 4.2629974
## 40 4.6862575 3.3050438 4.8596087 2.3255278 3.8771000 4.6574622
## 41 3.3348536 3.2474989 3.6318876 4.3573740 2.6266754 3.9409180
## 42 5.4225097 3.9255566 4.5720082 2.3854963 4.5436087 5.3245039
## 43 0.8168060 4.2028678 3.1798584 5.5720981 2.9962185 2.1320741
## 44 2.0495638 4.0738120 3.4677899 5.2064236 2.3661571 2.2488951
## 45 4.7985234 4.2471169 4.4973609 2.7140224 4.1215792 4.4193015
## 46 4.1876687 4.6271184 4.0734211 3.7077775 3.2693831 4.0604214
## 47 2.5113931 4.5836332 3.7499843 5.1212983 3.2304633 1.5819876
## 48 1.2907695 3.9807608 3.4559993 5.3741364 2.2810078 2.2761062
## 49 2.7665389 4.6904223 4.3173436 5.4014312 4.4110604 2.0308428
## 50 3.7348137 4.1383044 4.6815598 4.5814218 4.3479790 2.9018836
## 51 4.9599546 4.0709615 4.8134041 2.5062279 4.1165009 4.6790142
## 52 5.9366341 4.0267697 5.2680844 1.1597219 5.0095904 5.6046920
## 53 3.2383605 4.8482649 3.0857193 5.4126492 2.8977822 3.6762383
## 54 2.6035848 3.5422279 3.3667749 4.5751880 3.3532604 2.9150318
## 55 4.8557803 3.5689933 5.1517007 2.4631475 4.1512431 4.6420120
## 56 2.9983384 3.0081450 4.5272743 4.9859976 3.2587785 3.8874544
## 57 4.4811351 4.5107596 4.9061455 3.6351542 4.9682098 3.9484257
## 58 3.9097415 3.4348339 4.0071048 4.1259091 3.1480940 3.9188451
## 59 3.4715727 4.3986034 3.5422665 4.6975827 2.5181164 3.2561853
## 60 5.5455342 5.2176215 4.4939370 3.3273753 4.6559329 4.9742852
## 61 2.4081119 5.0899511 3.8196447 5.8351201 3.6492688 2.0527176
## 62 2.6859072 3.0552775 4.3342688 4.6598644 3.4019598 3.0216207
## 63 2.5438203 4.0000122 3.2413104 4.5237049 1.7857885 2.2501407
## 64 4.6178443 4.2576427 4.4705588 2.7544145 4.1181354 4.1153959
## 65 3.3472327 4.0418809 3.7423241 4.6761457 3.5247508 3.3383539
## 66 3.1013576 4.0902082 2.9630796 4.5466020 3.6274537 3.1291613
## 67 3.4344609 3.5695135 3.9295751 3.9597240 3.2127810 2.9545808
## 68 2.0043695 5.1315431 3.8047941 6.0867874 4.1715922 1.8876014
## 69 6.7676511 5.3641951 5.8987062 3.8613890 5.4750389 6.8065635
## 70 2.5547631 4.5097758 4.1490951 5.3547611 3.2250329 2.1479265
## 71 4.1888327 3.8751543 4.4764358 3.8644699 3.9876543 4.5377097
## 72 1.7646172 4.2393065 2.1051310 4.9408554 1.9412569 2.2584625
## 73 3.9937517 3.5255930 4.5380571 3.9506514 3.4306432 3.5743844
## 74 4.2752919 4.2133931 3.4381093 3.9178730 3.4551451 3.7890108
## 75 4.7922798 3.8285122 4.9092590 2.6473579 3.8514593 4.6108982
## 76 2.8652532 3.9955326 2.5437594 4.5072758 0.9410806 3.2736118
## 77 4.6624022 5.3793002 4.5554504 5.1141530 5.2288530 3.7913035
## 78 3.5476608 3.4897655 4.1512761 4.2042011 3.5186353 3.3971515
## 79 3.3320451 4.5651682 3.7561652 4.6421996 2.6392171 3.9489152
## 80 3.6278213 3.2501513 4.7713740 4.2150705 3.5856534 3.3156855
## 81 2.5718456 4.6732780 3.6407174 5.1878240 2.7612832 1.9356732
## 82 2.0430350 4.4252858 3.1510979 5.2532820 2.3584751 2.2576027
## 83 4.7972789 3.5812264 4.7204164 3.8386452 2.9853337 4.7993887
## 84 1.9354248 3.8045498 3.7664894 5.4367540 2.0795270 3.1370075
## 85 5.4264547 4.3910398 5.5223644 3.6474769 4.3515255 5.4282082
## 7 8 9 10 11 12
## 2
## 3
## 4
## 5
## 6
## 7
## 8 2.9892360
## 9 5.1470258 4.8548180
## 10 2.1102745 2.7480221 5.1202684
## 11 1.7729168 3.3419155 4.4733664 2.0204216
## 12 5.6078900 4.5636442 3.5834857 5.0129834 5.5219183
## 13 2.7041640 1.6973354 4.3541076 2.8365996 2.6538040 4.8886503
## 14 4.8706190 4.3984251 1.4424198 4.8903031 4.5200615 3.2815433
## 15 2.2294700 3.1240648 4.7986061 1.9773359 1.5201272 5.2571257
## 16 2.5596008 3.3067711 4.8839842 2.5288309 3.1306606 4.6240808
## 17 4.3285412 3.8840299 3.2859710 4.7163550 3.9342793 5.2014384
## 18 0.7116428 2.8345282 5.1382261 2.0162064 1.6347081 5.5949015
## 19 5.0998853 3.6630741 3.9250809 4.5436549 4.8484317 4.0693008
## 20 4.6174809 4.3762362 3.6900673 4.8977903 4.7023101 4.4055502
## 21 2.2536190 2.8951593 5.8337432 1.9283934 2.7682492 5.6465123
## 22 3.2946961 2.2416532 3.8755789 3.3118430 3.3376002 4.0326930
## 23 0.6860571 2.6746528 5.2059428 1.9240006 1.9096332 5.3968062
## 24 5.1120468 5.0133731 2.9300836 5.3200306 5.2565527 3.2366193
## 25 2.9303868 2.1437297 3.8021355 2.9444266 2.3808072 4.8115108
## 26 2.7895271 2.8316519 4.2189004 3.7862650 2.7461757 5.6718904
## 27 5.6573188 4.7590023 3.4189107 5.1417181 5.2122421 3.3608970
## 28 3.2806469 1.3372246 4.6832589 2.3933635 3.3091207 4.3286257
## 29 3.1007378 3.5348194 5.8855915 1.9486835 3.4189341 5.7614280
## 30 2.6865916 0.9068154 4.5460098 2.7517293 3.0098910 4.4538328
## 31 4.9906383 4.5871179 4.4339348 4.5814672 5.0205964 4.9241067
## 32 3.6546091 1.9342459 4.3496888 3.0158447 3.3247139 4.1538355
## 33 4.9745877 3.9949227 2.9180870 4.5862867 4.5573520 3.4358047
## 34 4.9561537 4.4086118 2.5179895 4.8725548 4.3169953 3.6972584
## 35 1.3701018 3.4541511 4.9552927 2.3794585 1.7381498 5.3846991
## 36 2.8136867 2.5804502 4.4167377 3.2412037 2.7351235 5.4123984
## 37 6.6916262 5.7411144 4.3238941 5.9225317 6.3415266 3.8525977
## 38 1.9770509 2.9934401 5.2431918 1.7411665 1.9947033 5.3566980
## 39 2.9603915 3.6968900 5.7744034 3.0965414 3.2031060 5.6024869
## 40 4.0083543 4.8228985 3.3878958 3.9304605 3.4200625 4.4577779
## 41 2.1383067 3.2479997 5.1543974 1.8749624 2.4257823 4.8800755
## 42 4.7044688 4.8496412 3.9526050 3.8337404 4.3476649 3.4648845
## 43 2.8184600 3.1948600 4.5006885 3.7032005 3.0371791 5.5243184
## 44 2.9841369 2.5754025 4.5345278 3.6428620 3.3396141 4.9510658
## 45 5.1396430 4.3415051 1.4358021 4.8271453 4.4731940 3.2795085
## 46 4.5976367 3.5034618 3.5409991 4.0265876 4.5456884 3.2281404
## 47 3.3410320 3.0376283 4.0296254 3.9232506 2.8338276 5.7989733
## 48 2.4827524 2.0150170 4.6664218 3.3255693 3.1803496 4.9391953
## 49 3.6647469 3.5760254 4.2552734 4.3176464 3.7906004 5.7333228
## 50 4.2935226 3.8775702 3.4752964 4.6369117 4.0668011 5.2966695
## 51 5.3270306 4.5792765 1.6211360 4.9999356 4.8609559 2.8168277
## 52 5.2217298 5.3134615 3.1066920 4.4972237 4.4553804 3.7061504
## 53 3.9168747 3.1910575 4.9182570 3.6242426 3.7803888 4.9702955
## 54 0.8962246 2.9809342 4.9146487 1.5446444 1.2393815 5.4028904
## 55 3.9532882 4.4970894 3.5551507 3.9390130 3.5512844 4.3331322
## 56 1.8050422 3.7781605 5.3681642 3.0775889 2.6981887 5.5899928
## 57 5.0994264 4.9271744 1.6717743 5.2831329 4.5523201 4.5558981
## 58 4.2500816 3.2454099 3.7508145 4.1518534 4.3121615 3.4152653
## 59 4.2392379 3.7382906 4.2992028 4.0366895 3.9672281 4.7847741
## 60 5.8465576 4.7638613 3.1578178 4.9764356 5.3103918 3.2604316
## 61 2.9049707 1.5333978 5.1909372 3.3627242 3.5690020 5.4577829
## 62 1.5621615 3.8319441 4.8501562 2.9713022 1.8570793 5.9247727
## 63 3.3854241 2.8625294 3.7242160 3.5542879 2.7806083 5.0616888
## 64 5.0432169 4.2726244 1.6843411 4.6850448 4.5300466 3.3794649
## 65 1.5968369 2.3956977 5.2787399 1.3984220 2.0687276 5.2226913
## 66 1.8803688 3.1015702 4.9374684 1.2614397 1.3760947 5.4146442
## 67 2.4435197 3.6394633 4.5120044 2.4497645 1.6157089 5.7034859
## 68 2.9949282 2.8746793 4.9842972 3.9227192 3.2986524 6.0657122
## 69 7.1427537 6.5936392 3.7492713 6.5706950 6.5838907 3.3430445
## 70 3.7794646 3.9628865 4.4953945 4.2886324 3.6822265 6.0600009
## 71 4.6461638 4.0212650 3.3679019 4.6599845 4.9913887 2.2688247
## 72 2.7347957 1.5515700 4.2756490 2.6128180 2.7052476 4.4945310
## 73 4.3090069 3.4307400 3.2475368 4.4022267 4.0522588 4.3227615
## 74 3.2983918 3.7413551 4.6660084 2.5564523 2.1078409 5.2987091
## 75 5.2115966 4.5508716 2.0168139 4.9787747 4.9096658 2.9318898
## 76 3.5902021 2.8018699 3.9576620 3.2928732 2.9852809 4.4073424
## 77 5.4686583 5.2171701 4.2328066 5.0722197 4.9132157 6.0495906
## 78 2.6645243 4.1426233 4.3777572 3.2247510 1.3308813 5.9838312
## 79 3.7420191 2.8428381 4.1171634 3.8609222 3.8704252 3.8203738
## 80 4.1327226 3.7335360 3.2426374 4.6413253 4.0281416 4.7365917
## 81 3.0526254 1.4541502 4.7093651 3.1622596 3.3683150 5.0811117
## 82 2.6746736 0.7778277 4.7795574 2.8162839 3.2512194 4.6617889
## 83 5.1335259 4.2511434 3.8082233 4.7370836 4.8387232 3.8843835
## 84 2.9946667 2.8777397 4.7987925 3.7850684 3.5711166 4.9517976
## 85 5.7918255 5.2446884 3.2593932 5.6337225 5.4896239 3.8193964
## 13 14 15 16 17 18
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14 4.3329793
## 15 2.8778542 4.7148600
## 16 3.6331496 4.5071365 3.0666584
## 17 3.5007427 3.2070385 4.0330509 4.4961697
## 18 2.5173834 4.9520788 1.9395986 2.6117352 4.1700210
## 19 4.3743477 3.2708387 4.5014842 4.1169001 3.0846125 4.9807694
## 20 3.8927622 4.0007290 4.8912177 3.9131025 3.6172480 4.5694821
## 21 2.8459002 5.7223443 2.5732318 2.9395843 4.9044928 1.7853983
## 22 1.9669644 3.8093091 3.4295684 2.7859307 3.3217334 3.1499277
## 23 2.6988723 4.8590108 2.0956242 2.3932932 4.3329425 0.6782529
## 24 4.7124077 2.9965224 5.5717070 4.4155314 4.7724502 5.2753302
## 25 1.2399603 3.7624327 2.7522790 3.7887521 3.2103144 2.8670187
## 26 1.7935141 4.1710767 3.2433505 4.1073436 3.0503403 2.7935090
## 27 4.9672453 3.3061212 4.9007038 4.4541950 5.0192442 5.6384132
## 28 1.9161183 4.3123159 3.2078922 3.4291936 4.2531833 3.2444503
## 29 3.8981975 5.4577374 3.2297140 3.0423282 5.3784402 3.2303728
## 30 1.3203287 4.1566916 3.0615572 3.3237005 3.8136595 2.6410155
## 31 4.6751587 3.8015594 5.1806925 4.5729559 4.4059929 5.2933964
## 32 2.5195244 3.9017741 3.2809991 3.8336330 4.1176917 3.6076345
## 33 4.2600437 2.5528708 4.5152370 3.9803571 3.1668434 4.9537363
## 34 4.0939730 2.8163949 4.2030966 4.4140618 2.8362176 4.8803603
## 35 2.9232326 4.8055441 2.5708664 3.0658449 4.6969735 1.6955967
## 36 1.0150014 4.5467268 3.1808346 3.9753667 3.5853452 2.7242906
## 37 6.1979256 3.7288481 6.2747891 5.7488982 5.8155507 6.7822450
## 38 2.7241548 5.1584955 1.1893151 2.8785258 4.4038853 1.6455901
## 39 3.7175857 5.5446696 2.8066834 3.6296901 5.1034965 2.8384477
## 40 4.6733620 3.1646814 3.7875460 3.5904366 4.7512308 4.1486813
## 41 3.3447208 4.7537124 2.8014242 2.8374960 5.1547173 2.4519492
## 42 5.0663964 3.4983589 3.9983263 4.0948595 4.8932981 4.7300631
## 43 2.0031083 4.4885872 3.7337840 4.1742386 4.0699294 3.0556787
## 44 2.6138006 3.9697817 3.2295444 3.8021873 3.8041770 3.2369691
## 45 4.1887666 1.5966451 4.5175382 4.7158663 2.9886269 5.0036403
## 46 3.9963450 2.8090811 4.4859894 3.6421063 4.5964902 4.6992818
## 47 2.3375122 3.9744490 3.1387167 4.3290566 2.6604409 3.2530106
## 48 1.8817509 4.2126658 3.5014439 3.5252908 3.9546198 2.7100956
## 49 3.0166099 4.2049333 3.9797271 3.6048500 2.9275972 3.6598866
## 50 3.6425559 3.1830711 4.1285212 4.3464636 0.9839624 4.2351588
## 51 4.6376655 1.3075386 4.9125092 4.5241643 3.6976194 5.3227389
## 52 5.3409981 3.2262503 4.4107245 4.2619527 4.6335116 5.0933069
## 53 2.8981474 4.7919587 4.0336832 4.4304147 4.8468144 3.9513205
## 54 2.4664168 4.8013870 1.8742909 2.6253237 4.3264418 0.9358441
## 55 4.6076897 3.2316481 3.6302746 3.1807898 4.4891453 3.9490426
## 56 3.5909818 4.9628315 3.3301282 3.2643130 5.1153971 2.3485964
## 57 4.3166234 2.3414763 4.7957627 4.9381380 2.7864932 5.0247697
## 58 3.6906234 2.9638631 3.9795366 3.8601901 3.0466370 4.3051925
## 59 3.8315283 3.8116790 3.8889212 4.2671801 4.5689149 4.5185429
## 60 5.0298845 2.8024227 4.8837708 5.0038398 4.2690752 5.7913706
## 61 1.9627372 4.7826599 3.3915207 3.5388923 3.6546003 2.7428419
## 62 3.3402556 4.5891551 2.7128286 3.2827761 4.3421240 2.0583260
## 63 2.4915390 3.4594326 3.1700012 4.1351202 3.2771211 3.4741886
## 64 4.2442143 1.3466833 4.5446933 4.4982298 3.0502699 4.9982303
## 65 2.6865901 4.9676479 1.8368001 2.3659083 4.3735936 1.2125517
## 66 2.4970867 4.9909801 1.7694682 2.9190238 4.4158344 1.6219670
## 67 3.4337088 4.2512161 2.0533747 3.2594072 3.9951806 2.5722485
## 68 1.7985072 5.0269159 3.5538159 4.2369379 3.5006195 2.7978169
## 69 6.5795598 3.9261787 6.5613510 6.0750266 6.3098918 7.2342838
## 70 3.5622321 4.0981654 4.1567432 4.5827918 4.0505012 4.1419263
## 71 4.2799130 2.5987473 4.8203761 4.0772612 4.3448844 4.8006426
## 72 0.8643937 4.1202905 2.9533613 3.4985927 3.7909669 2.6922785
## 73 3.6440532 2.6004330 4.0314430 4.1081839 1.7165765 4.2554460
## 74 3.6217278 4.5897497 1.4179308 3.7145783 4.2780307 3.1256600
## 75 4.7256083 0.9779800 5.0034346 4.5025191 3.8478158 5.3187069
## 76 2.4134094 3.8297761 3.4020506 4.1978364 4.1537714 3.6441553
## 77 4.7380936 4.2902196 5.0764337 5.3432692 3.6567103 5.5260491
## 78 3.4131809 4.4853177 2.3070286 3.9447096 3.9341474 2.6353355
## 79 2.9072642 3.7370916 4.0504154 4.3245191 4.7412546 3.7378079
## 80 3.6962671 2.6100391 4.1948159 4.2022595 1.6128980 4.1894556
## 81 2.2860149 4.0946127 3.1779200 3.4256305 3.4393262 3.0368783
## 82 1.6751054 4.2538197 3.1992523 3.2051508 3.8569564 2.6907104
## 83 4.6824871 2.9263588 4.9110853 4.6629421 3.9929889 5.2843637
## 84 2.7004124 4.3254995 4.0461626 3.9798124 4.5730535 3.3479312
## 85 5.3723720 2.6824809 5.6386495 5.3400499 4.6968316 5.9059723
## 19 20 21 22 23 24
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20 4.1999124
## 21 5.2123602 4.8406890
## 22 3.6784803 3.0491484 3.3996460
## 23 4.8259735 4.7205935 2.0127656 3.1897341
## 24 4.8598653 2.7937015 5.7568572 3.9276610 5.2339991
## 25 4.0352726 4.1167187 3.5931938 2.2957653 2.9615650 4.6668739
## 26 4.7317517 4.0722377 3.9174449 2.7841915 3.0042834 4.8372872
## 27 3.9331434 4.5827190 6.0023166 4.0504995 5.5338832 3.8888078
## 28 3.7721105 4.4698719 3.1684037 2.4735280 3.0998241 4.8478764
## 29 4.8396832 5.3762569 2.9944130 4.2810100 3.0942444 5.7457361
## 30 3.9815587 4.2326117 3.0656284 2.0444456 2.4816970 4.6852985
## 31 3.9593848 4.6290745 5.7121145 4.4546017 5.1390258 4.4424451
## 32 3.5152416 4.9545716 4.0269262 2.8011155 3.3615471 5.0907540
## 33 1.7834187 3.4043002 5.4547768 3.3784148 4.8209589 3.7715710
## 34 3.0914182 3.0950999 5.5148288 3.3737600 4.9201007 3.7628634
## 35 5.4795255 4.8763485 2.9843320 3.4598301 1.6093464 5.0116268
## 36 4.9296565 3.8250546 3.2045272 2.4464391 3.0397016 4.7092457
## 37 4.2362128 5.9799138 7.0829974 5.5917511 6.5368629 4.8874972
## 38 4.8819517 4.7208453 1.6957901 3.3485569 1.8996039 5.5201842
## 39 5.3902123 5.4573958 3.1853010 4.0723900 2.7891715 5.9493245
## 40 4.7847793 5.2506054 5.0933962 4.1918086 4.0209040 4.3206562
## 41 5.0538008 5.2669756 3.1874076 3.6477660 2.0361788 5.1139181
## 42 4.1597657 5.4253267 4.9032977 4.7321287 4.5705050 4.6689011
## 43 5.4333906 4.1348951 4.0029649 2.9636793 3.1923834 4.4730409
## 44 4.3125033 4.5881014 4.2926803 3.1081697 3.0407142 4.7660901
## 45 3.0417312 4.0012479 5.4522539 3.6814788 5.0356952 3.6417805
## 46 3.5434639 4.6689363 5.0062265 3.2722161 4.4694048 3.7102887
## 47 4.2031914 4.3804260 4.2963163 3.1380095 3.4457892 5.2187719
## 48 4.6048391 4.2602127 3.6321205 2.5359237 2.5271802 4.5116878
## 49 4.2807869 3.1834310 4.3205407 2.6717279 3.8809794 4.4497947
## 50 2.9221878 3.6027126 4.9483638 3.4789190 4.3500690 4.6761485
## 51 2.9854988 3.8224348 5.8335441 3.9059168 5.2402448 2.9326364
## 52 3.8744608 4.7777027 5.3805138 4.7218904 5.0643772 4.3069717
## 53 5.0441710 4.9778109 4.2468186 3.3836267 3.8977741 5.1372198
## 54 5.0399242 4.5432633 2.0002652 3.1510789 1.1518286 5.0534112
## 55 4.2619621 4.9805928 4.7814830 3.9455056 3.8089191 4.3852306
## 56 5.7129953 5.2765119 3.7186921 3.9478266 1.9866322 5.1379138
## 57 4.0572992 3.3240225 5.6448078 3.9795904 5.2264488 3.3346331
## 58 2.5471178 4.0999833 4.8348497 3.1531278 4.0774338 4.2922283
## 59 4.1579829 4.9307522 5.3703468 3.9581253 4.3085363 4.7217661
## 60 2.9729480 4.8415526 5.9052871 4.5505880 5.7222837 4.3649127
## 61 4.1452021 4.2136362 2.9585832 2.6527699 2.7681951 5.2180509
## 62 5.3642060 4.9588614 3.7075517 3.8781930 2.0040346 5.1278935
## 63 3.9321824 4.6447302 4.5406474 3.0757367 3.4230496 4.8848411
## 64 2.7776759 3.8991406 5.4396570 3.7577971 4.9908318 3.4124584
## 65 4.4619375 4.8113922 1.4336238 3.1341482 1.0708918 5.4753446
## 66 4.9928937 4.6105453 1.7588335 3.2268120 1.9507550 5.2902110
## 67 4.4126779 5.1246359 3.7287127 3.9149232 2.5403589 5.4474362
## 68 5.1727407 3.9817811 3.3270883 2.8885828 3.1765587 5.2035590
## 69 5.2341882 5.2914924 7.6667646 5.7543207 7.0963617 3.8779096
## 70 4.8577417 4.9483276 5.2840415 4.1263461 4.0966598 5.0209079
## 71 3.9481851 3.9353241 5.1882695 3.6478640 4.5882716 2.6505656
## 72 4.2380726 4.0705421 3.0728300 1.9989557 2.6911195 4.5363766
## 73 2.0364116 3.9970271 4.9888738 3.2027100 4.1580717 4.5714043
## 74 4.3300898 5.4611123 3.7313868 4.0240447 3.1526463 5.9147977
## 75 3.0825554 4.1914027 5.9596655 4.0689874 5.1494216 2.9895774
## 76 4.3769120 4.8265987 4.3600862 2.9099020 3.5308677 4.7971173
## 77 4.2982203 4.5218643 5.8466183 4.7829481 5.6960008 5.2294576
## 78 5.1532668 5.1722552 4.0199720 3.9846816 2.8250564 5.5932454
## 79 4.9176444 5.1081205 4.2490558 3.2199034 3.5554035 4.3593381
## 80 2.8596764 3.8650383 5.1795068 3.3557111 4.1191846 4.3756369
## 81 3.3508339 4.4598602 3.5821586 2.7730709 2.8740407 5.0952183
## 82 3.8741621 4.2609999 3.0809432 2.2753627 2.4817131 4.7546227
## 83 2.9281004 5.1465251 5.9676691 4.1814821 4.9778691 4.7771770
## 84 5.1216744 4.7447897 4.3771717 3.1352719 3.0801078 4.5524905
## 85 4.2276083 5.2460854 6.5816641 4.8558542 5.7205832 4.1306933
## 25 26 27 28 29 30
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23
## 24
## 25
## 26 1.6258507
## 27 4.5004596 5.2279934
## 28 2.0397328 3.2307554 4.5366142
## 29 3.9845943 4.6210966 5.5552051 3.0185776
## 30 1.6566745 2.3454822 4.7577085 1.4494947 3.7591627
## 31 4.2794327 4.8457031 5.1560461 3.9043590 4.0825116 4.4720944
## 32 2.0079236 3.3210493 4.2472468 1.7254453 4.0876588 1.7380966
## 33 3.7334263 4.4538754 3.2682282 3.8920059 5.1436676 3.9616356
## 34 3.5825758 4.0623024 3.4740028 4.3694575 5.7048519 4.1904490
## 35 2.9060645 3.0599124 5.6865505 3.4721203 3.7483272 2.8718028
## 36 1.5935127 1.5520193 5.3190629 2.6137116 4.0814202 2.1677624
## 37 5.6689116 6.5905754 4.0934519 5.2886879 6.1387990 5.7233630
## 38 3.0565838 3.4098149 5.3147975 3.0877889 2.8207802 3.0092639
## 39 3.9082807 4.1684428 5.7943382 3.9355764 4.0757818 3.6073930
## 40 4.0560527 4.5631814 3.6250920 4.6084855 4.7238649 4.5055063
## 41 3.1977728 3.8920955 5.3432261 2.9592241 3.0966781 2.8304553
## 42 4.7775691 5.6132233 4.3324020 4.4446371 4.2774968 4.8254057
## 43 2.0565123 1.6695099 5.5616111 3.1377685 4.4636036 2.4798075
## 44 2.2408851 2.2092922 4.6474771 2.8038705 4.1545511 2.1426525
## 45 3.7343873 4.3620976 3.2725003 4.2904046 5.6186526 4.2547178
## 46 3.6595161 4.4836056 2.6067878 3.1397548 4.2371272 3.5059044
## 47 1.7117910 1.2740157 4.8743971 3.3676541 4.6471124 2.7954311
## 48 2.0380466 1.9442676 5.1601054 2.4152341 4.1007341 1.3093188
## 49 3.0728475 2.4929242 4.7299780 3.8445945 4.4831055 3.5107747
## 50 3.3373213 3.1665874 4.9638160 4.1348565 4.9425499 3.8761053
## 51 4.1294877 4.7664625 2.5655245 4.4127423 5.5485464 4.4755480
## 52 4.9292618 5.6994013 3.5735300 5.0901290 5.2379307 5.2990808
## 53 2.8419995 3.6267550 5.3038876 2.8409439 4.4953850 2.8227141
## 54 2.6461493 2.8805432 5.4717971 2.9896236 2.8544328 2.6663763
## 55 4.1535193 4.5502476 3.2726661 4.5827366 4.7499580 4.3635324
## 56 3.5137624 3.4696905 5.9520148 3.9029276 4.0903420 3.1832760
## 57 3.9766187 3.9819610 3.9245067 4.9311908 5.7828529 4.7722335
## 58 3.4233618 3.9697646 4.3358774 3.3311781 4.7348097 3.1446283
## 59 2.9909334 3.6789121 3.7567372 3.2376322 4.1776764 3.4532467
## 60 4.5929391 5.4902583 2.9806434 4.3475943 5.1200171 4.9139392
## 61 2.6202414 2.4397920 5.3111877 2.4895341 3.7562345 1.8974482
## 62 3.0129567 2.7377069 5.6361528 3.9180909 3.7858246 3.3272838
## 63 1.3370475 2.0398958 4.3621173 2.7755965 4.3855791 2.4033775
## 64 3.7728067 4.3697897 3.1006214 4.1003112 5.1106084 4.2503400
## 65 3.0167995 3.4326053 5.3510017 2.7667037 2.7396733 2.4973302
## 66 2.7159415 3.2834518 5.4238612 2.8958057 2.6996812 2.9497493
## 67 2.7727871 3.1854341 4.8995384 3.4858306 3.1077444 3.4384608
## 68 2.5136302 1.6096762 5.8401762 3.4484719 4.6186509 2.6940552
## 69 6.0120800 6.8411250 3.1797364 6.1012046 7.0958338 6.3573915
## 70 2.8029334 2.6764791 5.1167109 3.7032969 4.2704620 3.5805720
## 71 4.2577141 4.6392641 3.8191942 3.9618657 5.0455154 3.8373283
## 72 1.1572450 2.1717695 4.7383148 1.3906306 3.6934965 0.9263121
## 73 3.1786023 3.5114499 4.4759599 3.7212883 5.0719226 3.3751042
## 74 3.0486862 3.8900573 4.6061770 3.5494112 3.6411956 3.6787898
## 75 4.1526878 4.7485653 2.9051941 4.3413582 5.3866984 4.3927481
## 76 1.6133008 2.9045607 4.5260300 2.3771063 4.5308345 2.1523966
## 77 4.3216943 4.6838909 5.4626928 4.6797356 4.7210765 5.2135861
## 78 2.7765123 2.8922918 5.3755117 4.1831851 4.4778876 3.7123324
## 79 2.9290349 3.4906541 4.5274336 3.0498181 5.0272288 2.3909295
## 80 3.2157774 3.1408202 4.7859601 4.0505795 5.2302523 3.5178161
## 81 2.2071916 2.5009486 4.6017035 2.0629236 3.4602664 1.7629071
## 82 2.0301981 2.4708426 4.8193041 1.4972356 3.4580922 0.7377685
## 83 3.9850252 4.8435476 4.5231119 3.9608713 5.2970892 4.0325920
## 84 2.5707948 2.6474879 5.3828674 2.9811531 4.6376557 2.0645815
## 85 4.8180260 5.3770991 4.1534592 5.0683571 6.1887065 5.0085645
## 31 32 33 34 35 36
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
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## 15
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## 23
## 24
## 25
## 26
## 27
## 28
## 29
## 30
## 31
## 32 4.4534597
## 33 3.7723367 3.4291711
## 34 4.4499407 3.9382947 1.9196619
## 35 5.1177666 3.5056487 5.0139507 4.8628827
## 36 4.6682469 3.3333722 4.6840088 4.3111501 3.0371705
## 37 4.7051253 4.9115359 3.8674151 4.8116812 6.5565486 6.6180053
## 38 5.2128573 3.6919617 4.9788984 4.7107159 2.5936599 2.9516575
## 39 5.8810461 4.0945993 5.4039158 5.2440472 3.2074083 4.0570639
## 40 4.9337035 4.1330876 4.1193666 4.2386082 3.6939428 4.8638767
## 41 4.6394375 2.9482566 4.7060434 4.9955085 1.5666722 3.7328464
## 42 4.2435919 4.4359295 4.1104179 4.3635541 4.6417062 5.4136265
## 43 4.4832281 3.5716626 4.9023496 4.5398796 2.6763080 1.4914276
## 44 4.1324862 2.7272905 4.1128271 4.0120275 3.1834955 2.8363813
## 45 4.5591288 3.8962818 2.5986261 2.6218558 5.1298388 4.5016935
## 46 3.7666291 3.1805161 3.3815225 4.1779884 4.6905132 4.4228312
## 47 4.8259079 3.2162577 4.0873488 3.7884353 3.6908874 2.2985454
## 48 4.3973399 2.6267200 4.3643440 4.4542299 2.6221902 2.2028184
## 49 4.3523652 4.4151199 4.1727548 3.9733764 4.3289429 2.7143370
## 50 3.7380429 4.2253542 3.1520083 3.1117606 4.7974410 3.6496995
## 51 4.1872308 4.0429297 2.1157455 2.6346390 5.2948176 4.9452497
## 52 5.2575730 4.7675611 3.3619662 3.6681782 5.1541053 5.6806036
## 53 4.8055784 3.0308873 4.7113198 4.7712799 3.6804595 3.2105942
## 54 4.8524424 3.4399192 4.8418463 4.7586969 1.2625974 2.5660515
## 55 5.3616207 4.0889476 3.8440423 4.1027602 3.9731406 4.9426466
## 56 5.1720875 3.8107516 5.2489914 5.2750622 1.1943781 3.7399961
## 57 4.6292691 4.9752263 3.4954466 2.9877150 5.2838588 4.1829672
## 58 3.3866963 3.0500461 2.5726218 2.8546713 4.3384141 4.1782769
## 59 3.5198238 2.9944887 3.5870415 3.7817467 4.1699541 3.9990357
## 60 3.9428413 4.3395054 3.0522137 3.4618463 5.9931278 5.3673714
## 61 4.8806184 3.2584151 4.5853671 4.7940243 3.7961077 2.3888950
## 62 4.8305347 3.8865078 4.9396389 4.8041104 1.5064851 3.2450462
## 63 4.1647210 2.1257373 3.5238686 3.5278386 3.2781299 2.7277639
## 64 3.7811394 3.9615381 2.4797858 2.8407212 5.1698701 4.4796445
## 65 5.2117075 3.1422201 4.6799285 4.9047181 2.3346844 3.2128310
## 66 4.9620492 3.5120570 4.8776121 4.7691458 2.1202306 2.6195892
## 67 4.4335197 3.3317740 4.2371523 4.3539218 2.6321296 3.5426951
## 68 5.4153818 4.0935957 5.1720744 4.7786183 3.6322168 1.4283415
## 69 5.6249469 5.6527283 3.8858984 3.9647660 6.7397295 6.8366851
## 70 3.5191445 3.8241475 4.4778608 4.5549885 3.9344922 3.2924003
## 71 3.7875475 4.1147047 3.5628435 3.7462327 4.6771448 4.5868953
## 72 4.2885317 1.9204785 4.0170585 4.0366313 2.7152199 1.5749753
## 73 3.8205117 3.2135815 2.2101462 2.6479426 4.5190329 4.0555953
## 74 5.1543875 3.1933043 4.2704506 4.0709145 3.3173876 3.9663317
## 75 3.6689927 3.9437427 2.3116609 3.0296279 5.1529156 5.0226082
## 76 4.4586663 1.5280879 3.7716645 3.7848674 3.0089626 2.8937886
## 77 2.8897475 5.2889320 4.2665380 4.2955360 5.7915472 4.4408479
## 78 5.4534968 3.7422413 4.6830341 4.2738987 2.3785747 3.4137920
## 79 5.4052016 2.6744993 4.6329315 4.7396148 3.4760590 3.4919823
## 80 3.7300207 3.6550397 2.7053422 2.8301805 4.3395701 3.8996849
## 81 4.1711014 2.3712627 3.7939762 4.2921947 3.7321089 2.8177696
## 82 4.2668599 2.1052346 4.0396949 4.4167490 3.1386674 2.3721609
## 83 3.3413517 3.1443999 2.4984089 3.4669984 4.8825909 5.1614144
## 84 4.5249723 2.8405945 4.6092764 4.6861248 2.6374567 2.9459530
## 85 4.6271631 4.5190494 3.5961826 4.0355344 5.5771320 5.6787265
## 37 38 39 40 41 42
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
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## 20
## 21
## 22
## 23
## 24
## 25
## 26
## 27
## 28
## 29
## 30
## 31
## 32
## 33
## 34
## 35
## 36
## 37
## 38 6.6623204
## 39 6.0048238 2.7167355
## 40 4.7702222 4.3824499 4.7949141
## 41 5.8267124 2.8726000 3.3347533 3.5670268
## 42 4.2203882 4.2495321 4.8553102 3.2764350 4.0412829
## 43 6.6447540 3.6152013 4.3310605 4.7044173 3.4628722 5.6037359
## 44 5.8265197 3.4558572 3.9241087 4.3334625 3.2989593 4.9425656
## 45 4.0269286 4.9812753 5.5337314 3.5942103 5.1339536 3.5381543
## 46 3.7026396 4.6713013 5.1487220 3.1949695 4.0988270 3.5598169
## 47 6.2964092 3.6080919 4.4253013 4.4213658 4.2778326 5.4857249
## 48 6.1047923 3.4304673 3.8643462 4.5455565 2.9145609 5.2441537
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## 50 5.6498222 4.4130775 5.1858901 4.7685416 5.1254841 4.7807042
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## 59 4.8780690 4.3604134 4.8707713 4.0050085 3.7515281 4.6779924
## 60 3.4622295 5.2275060 5.9147289 4.2886496 5.5227728 2.9637632
## 61 6.5493775 3.0757245 3.9506256 5.3207823 4.0322137 5.5164689
## 62 6.5895391 2.9873726 3.6142729 3.5142380 2.3854214 4.8564048
## 63 5.3825724 3.7884206 4.3484716 3.7391602 3.4111465 4.8555438
## 64 3.7108279 4.9272146 5.5644022 3.5416864 5.0509509 3.2961494
## 65 6.3502543 1.5756947 2.7727461 4.1839773 2.3122314 4.3205358
## 66 6.4849398 1.4247909 3.1337625 4.0579072 2.4606580 4.2961636
## 67 5.8356910 2.7800919 3.7143418 3.0953740 2.6820440 4.1565545
## 68 7.3158744 3.2487173 4.2713820 5.4767539 4.5042863 6.0759068
## 69 4.0088834 6.9923165 7.2525795 4.7484713 6.3084605 4.8656433
## 70 5.9804168 4.4755297 5.1326268 4.3871961 4.1145416 5.4874059
## 71 4.2561227 4.7870921 5.1106274 4.1409131 4.4129235 3.3346954
## 72 5.7452151 2.8882585 3.6999775 4.3899500 2.8154875 4.7471405
## 73 4.7721688 4.5110105 4.9260566 4.2740887 4.5116054 4.1968116
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## 75 3.1329281 5.4293664 5.7754547 3.2842616 4.8347013 3.3891355
## 76 5.2537677 3.8475398 4.2729633 3.8945964 2.8548655 4.6626765
## 77 5.7975580 5.1987187 6.2891276 5.4250676 5.8357670 4.9916705
## 78 6.5231250 3.1204677 3.8695453 3.3062607 3.1606090 4.8158082
## 79 5.4010817 4.1630046 4.3725490 3.9731975 3.4398911 4.5731660
## 80 5.1806980 4.6294580 5.0207184 4.2782700 4.5593218 4.5580464
## 81 5.6549931 3.2876501 4.0003440 4.6205712 3.6100335 4.9514078
## 82 5.7656498 3.0529836 3.6930945 4.6718149 3.0162075 4.8974413
## 83 3.7794125 5.4389682 5.5847515 4.1860385 4.2518805 3.8933700
## 84 6.0800602 4.0922237 4.2678351 4.5060922 2.8062549 5.3889407
## 85 2.1193355 6.0844374 5.2457077 4.0359290 5.2843523 4.1987800
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## 44 2.4632749
## 45 4.9018397 4.5660927
## 46 4.5241715 3.7542917 3.2186948
## 47 2.7289616 2.5198432 3.9905014 4.3729169
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## 50 4.0600311 3.6458782 3.2407411 4.3607599 2.7571428 3.9210025
## 51 5.1092207 4.5662516 1.4254228 2.7619998 4.4633044 4.7828186
## 52 6.0479842 5.6577961 2.7203324 3.9324906 5.3414082 5.8020885
## 53 3.2855480 3.5540330 4.8727399 4.2702040 3.9608334 3.1275304
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## 55 5.0284954 4.3689327 3.4057206 3.1494642 4.3114795 4.5563692
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## 60 5.8115351 4.9291392 2.4557265 2.9887897 5.0167380 5.4739352
## 61 3.1167948 2.7084273 4.7945527 4.1930707 2.7465145 2.2160858
## 62 2.7382131 2.8498323 5.1334631 4.7363275 3.1510542 2.7778961
## 63 2.6550254 2.0443962 3.7549774 3.6279039 1.6736096 2.4291224
## 64 4.8193874 4.3533217 1.0736024 2.7532473 3.9747547 4.6001398
## 65 3.7465472 3.4627821 4.8731317 4.3360587 3.6320158 3.0307742
## 66 3.2359763 3.7701603 4.8091436 4.5526491 3.5299913 3.3615467
## 67 3.6335523 3.1511700 4.4826408 4.1952793 2.8484864 3.5016124
## 68 2.3207201 3.1797780 4.9530751 5.0521867 2.3550290 2.5837715
## 69 6.7333698 6.2208187 4.1618429 4.4774171 6.6709971 6.6002655
## 70 2.7624826 2.4011950 4.8712908 4.1637384 2.5895455 3.0021610
## 71 4.4391757 3.7606096 3.3259176 2.8368100 4.9374497 3.8501361
## 72 2.0040578 2.3578495 4.1388825 3.5818679 2.6655803 1.6089838
## 73 4.2874867 3.3958974 2.7146617 3.7744111 3.1501339 3.6361750
## 74 4.4206451 3.6616088 4.3404709 4.4293601 3.4256809 4.2039027
## 75 4.9702369 4.2535128 1.9951808 2.4869003 4.5109957 4.5429144
## 76 2.7692478 2.7206122 3.9625833 3.6354417 3.0393416 2.5244971
## 77 4.8421402 4.9701353 4.3344728 4.8417749 4.2791613 5.3272501
## 78 3.4378500 3.5692128 4.5381389 4.9895252 2.7519028 3.6779136
## 79 3.4356221 3.2715966 3.9071886 3.2629964 3.9228351 2.6714464
## 80 3.8756489 3.1349882 3.1141252 4.0510130 2.9441531 3.4031508
## 81 3.2506662 2.0676749 4.2781643 3.4248728 2.3495723 2.1472856
## 82 2.6751094 2.0322333 4.4569389 3.4442712 2.8624563 1.3447644
## 83 4.9692538 3.9503897 3.5432668 3.5346778 4.6253011 4.2591597
## 84 2.0148757 2.0180503 5.0140889 4.0825718 3.4592816 1.1438724
## 85 5.5137059 4.8948480 3.2752528 3.6745492 5.2288510 5.1079418
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## 50 2.6174387
## 51 4.5405615 3.7016536
## 52 5.5182271 4.7427529 2.6128750
## 53 4.5918313 4.9004568 5.0404575 5.7013295
## 54 3.7564939 4.3348901 5.1607539 4.8866358 3.6354803
## 55 4.5221099 4.5574332 3.2609946 2.7519498 5.1384212 3.9136837
## 56 4.6886823 5.1217024 5.5602940 5.6357146 4.0881735 2.1624935
## 57 3.4643631 2.8344158 2.5171500 3.7055016 5.3326526 4.9429587
## 58 4.1479273 2.9819407 3.3743902 4.4715855 4.2240734 4.2718135
## 59 4.1262060 4.2525475 4.0487570 5.1299220 4.0081005 4.1455908
## 60 5.0496603 4.0563495 2.2996234 3.1642981 5.3728820 5.5601948
## 61 2.8141462 3.5272732 5.0887252 5.8930915 3.8872187 3.1350122
## 62 3.8409206 4.2802217 5.2192844 5.2558896 4.1685604 1.8279973
## 63 3.4186695 3.3154334 3.9616790 4.9343714 3.3564096 3.2691531
## 64 4.0528925 2.9602811 1.2406542 2.8322553 4.8740827 4.8478907
## 65 4.0804442 4.4072518 5.1542617 4.7598358 3.9119084 1.5259588
## 66 3.9388252 4.4521112 5.1792183 4.6767634 3.6920610 1.0560506
## 67 3.8678373 3.8592761 4.6195306 4.3402444 4.1848044 2.2546623
## 68 2.4806725 3.5899926 5.4635418 6.2181780 4.0561071 3.0763543
## 69 6.7005586 6.3207309 3.1264792 3.9790568 6.3680990 6.8587004
## 70 3.2386514 3.6067546 4.7635740 5.8931534 4.2195285 3.8371878
## 71 4.5743417 4.1898424 2.9288676 4.2833850 4.6521278 4.6804859
## 72 3.4015983 3.8685702 4.4279948 5.1878903 2.5547227 2.4647829
## 73 3.6489628 1.8453676 3.0799532 4.1986350 4.5095282 4.3436345
## 74 4.6056552 4.3689156 4.6836759 4.0219268 4.3194074 2.8709184
## 75 4.6195472 3.7113451 0.9939940 3.0717262 4.9716638 5.1233952
## 76 4.3702739 4.3456792 4.1615411 4.9318013 2.7962340 3.2530011
## 77 3.7736133 3.0284589 4.5131303 5.2438768 5.4517475 5.1585371
## 78 4.1512365 4.1679977 4.9409251 4.6276983 4.3270412 2.4227472
## 79 4.7937249 4.9566571 4.1423373 5.0192342 3.5509258 3.7003674
## 80 3.3070307 1.6081108 3.3718323 4.6305974 4.6113177 4.2774095
## 81 2.9891827 3.2002291 4.4080054 5.3300443 3.6597834 3.2184958
## 82 3.3100489 3.7597958 4.5844835 5.4666617 3.1070016 2.7919184
## 83 5.2197810 3.9163372 3.2832741 4.3823328 4.6137502 5.0441780
## 84 4.1225459 4.5753818 4.9681867 6.0276167 3.2576397 3.1886233
## 85 5.5744998 4.6895110 2.9083993 4.1299098 4.2455954 5.7119430
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## 56 4.1774314
## 57 3.9910011 5.7649632
## 58 4.3180500 4.3976587 4.2161015
## 59 4.3102916 4.1844731 4.7513016 3.5146563
## 60 4.1911643 6.3686692 3.5001219 3.4874876 4.1830191
## 61 4.8963050 4.0764454 4.7928244 3.8313256 4.2555502 5.3183305
## 62 3.8035389 1.5994506 4.9569907 4.3990880 3.7430698 5.9409413
## 63 3.9253252 3.5822271 4.0698334 3.3791102 2.3398958 4.5657276
## 64 3.4247095 5.5378565 1.9974552 3.1944852 4.0618720 1.9034570
## 65 3.8324340 2.8959945 5.2807531 4.0818760 4.4688991 5.3694727
## 66 4.1245949 3.1401730 4.9145928 4.5161491 4.3978781 5.3262366
## 67 3.2751979 3.0618567 4.6053596 4.1650241 3.1929722 4.9081917
## 68 5.2757284 4.1791409 4.4001342 4.5877694 4.7698707 5.9535289
## 69 4.9418904 6.9324230 4.9184747 5.2212313 4.9397385 3.9562194
## 70 4.7823260 3.9479395 4.4509700 4.2203777 2.3482763 5.1930039
## 71 4.1200035 4.6536650 3.8868926 2.6094638 4.1268934 3.3828301
## 72 4.4495582 3.2696134 4.5164659 3.3812371 3.3547791 4.8204252
## 73 4.0144942 4.7100892 3.4523990 1.8485752 3.9016043 3.6789040
## 74 3.4996624 3.9867239 4.9070942 4.1075398 3.5848465 4.5010817
## 75 3.3048791 5.2468685 2.9534498 3.0812185 3.7031140 2.4623621
## 76 4.2416324 3.4402822 4.7333519 3.4598612 2.9164065 4.7574600
## 77 5.7144505 6.2865683 3.6706867 4.5243776 4.4789992 4.0282430
## 78 3.5449296 3.0601665 4.5566035 4.6250842 4.0410162 5.6293175
## 79 3.9528248 3.6576026 4.7483436 3.9142139 4.2593659 4.9150269
## 80 4.1492754 4.4193092 3.3098042 2.1850929 3.8444315 4.2010162
## 81 4.2777895 3.8855317 4.5723210 3.2115401 3.1391951 4.5857660
## 82 4.4587424 3.3114098 4.8499722 3.1617658 3.4041036 4.9086320
## 83 4.4014284 4.8447207 4.7863531 2.2143402 3.5071672 3.7376486
## 84 4.7499858 2.3642226 5.2831591 3.6362456 3.3664212 5.8184155
## 85 4.1871139 5.6159623 4.1817628 3.8792312 4.5377320 3.8266403
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## 62 3.8084184
## 63 3.3104935 2.9304330
## 64 4.6209353 5.0093546 3.7114794
## 65 2.7187433 2.8441542 3.6209855 4.8477866
## 66 3.3685441 2.7082282 3.5289396 4.7803989 1.7025601
## 67 3.8598012 1.9504420 2.4994205 4.2803639 2.6776152 2.4824285
## 68 1.9560568 3.6071888 3.4095711 4.9461805 3.4097346 3.2739138
## 69 7.3571399 6.8537186 5.7859063 4.1270355 7.0448525 6.8381244
## 70 3.8402999 3.0263537 2.1867882 4.3983401 4.5288332 4.2473899
## 71 4.4552306 4.8663310 4.4103063 3.0143517 4.7141109 4.9710204
## 72 2.3300359 3.2379024 2.2384915 4.1461783 2.7029451 2.5749747
## 73 3.7318690 4.2931648 2.9436240 2.7029338 4.1500118 4.5363249
## 74 4.2855801 3.2857617 3.0580068 4.3758182 2.8293771 2.6395876
## 75 5.0798827 4.9843863 3.8122330 1.5309923 5.1710878 5.2742315
## 76 3.8221044 3.4341098 1.7367385 4.1168644 3.6119422 3.3896958
## 77 5.0895063 5.3154227 4.4047797 3.6769018 5.6065681 4.9127807
## 78 4.3236279 1.9661000 2.6556285 4.6897078 3.1567098 2.6938980
## 79 3.6497960 4.0646736 3.3000897 4.1246994 3.6809320 4.0113951
## 80 3.7643856 3.9030921 2.8708662 3.0094259 4.3544889 4.6351495
## 81 1.4856458 3.5103503 2.3702633 3.9994936 2.8035524 3.4768272
## 82 1.4515947 3.3813018 2.6179787 4.3001966 2.5037589 3.1258571
## 83 5.1327096 4.8543543 3.4613315 3.3855498 4.9899921 5.2600634
## 84 3.3484954 2.8955041 2.6588097 4.9567664 3.6894610 3.8897293
## 85 5.8381981 5.5060573 4.4661259 3.1872909 5.7958003 5.9037995
## 67 68 69 70 71 72
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## 68 4.0540717
## 69 6.3529473 7.6386887
## 70 2.9723542 3.8285325 6.4327427
## 71 5.0115820 5.0364868 4.4495499 4.7883519
## 72 3.3032554 2.5547644 6.1771767 3.3779446 3.9615044
## 73 3.8157277 4.2523919 5.5972812 3.9810094 3.6231894 3.5696642
## 74 1.9122201 4.5483321 6.1009755 4.2227157 5.1548987 3.5130849
## 75 4.4895091 5.5753336 3.3467998 4.3832515 2.5677021 4.4053422
## 76 3.2562841 3.9493923 5.4842000 3.4196846 4.2655034 1.7863766
## 77 4.5029791 4.9916302 6.3409828 3.8936220 5.1614723 4.7915266
## 78 1.7406385 3.8707379 6.5965222 3.6346204 5.4478998 3.4497751
## 79 4.3471528 4.0266194 5.8494231 4.5655625 3.4450085 2.5567320
## 80 3.7776011 4.0106740 5.8229364 3.5056605 3.6433281 3.6658630
## 81 3.1129389 2.8862838 6.6236634 3.0317796 4.1576475 2.2457494
## 82 3.4574282 2.6873041 6.5656064 3.4229423 3.8150092 1.4297099
## 83 4.3262348 5.8558756 4.7423619 4.3512807 3.6344907 4.1463318
## 84 3.8291241 3.5514688 6.4167615 3.1893834 3.9520730 2.1944041
## 85 5.1791613 6.2411454 4.2804571 5.1289571 3.6093270 5.0255950
## 73 74 75 76 77 78
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## 74 4.0361682
## 75 2.9778068 4.7685489
## 76 3.5671660 3.3182492 4.0579365
## 77 4.1109111 4.9957306 4.4967121 5.1412781
## 78 4.0914352 2.3589493 4.9650504 3.1838577 5.2080597
## 79 4.1874136 4.4410312 4.0212847 2.6813201 6.2822344 4.2752615
## 80 1.0341353 4.3352097 3.1475315 3.7124226 4.0406264 3.9406958
## 81 3.0440017 3.6233222 4.2661940 3.1469856 4.6499370 3.9047117
## 82 3.4116047 3.8661146 4.4388331 2.7028334 5.0911248 3.9915417
## 83 2.4685458 4.5104868 2.7568684 3.3892993 4.8432292 4.8649000
## 84 4.0460442 4.5595378 4.6125203 2.3755704 5.8069900 3.8759405
## 85 3.8616394 5.3878717 2.6036400 4.5115504 5.5106423 5.4533464
## 79 80 81 82 83 84
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## 80 4.3055998
## 81 3.4513833 3.1742792
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## 85 4.4769056 3.9835404 5.0870076 5.1320769 3.4251649 5.0236666
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## 1051 1052 1053 1054 1055 1056
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## 1057 1058 1059 1060 1061 1062
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## 1063 1064 1065 1066 1067 1068
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## 1069 1070 1071 1072 1073 1074
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## [ reached getOption("max.print") -- omitted 1105 rows ]
matstd_heart <- scale(heart)
fviz_nbclust(matstd_heart, kmeans, method = "gap_stat")
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
Inference: * By performing gap statistic analysis, we determine the optimal number of clusters. * Based on the Screeplot , we are considering 2 clusters.
Dendogram - - To visualize the different possible clusters
res.hc <- heart %>% scale() %>% dist(method = "euclidean") %>%
hclust(method = "ward.D2")
fviz_dend(res.hc, k = 2, cex = 0.5,
k_colors = c("#2E9FDF", "#00AFBB", "#E7B800", "#FC4E07"),
color_labels_by_k = TRUE, rect = TRUE)
## Warning in get_col(col, k): Length of color vector was longer than the number
## of clusters - first k elements are used
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
## Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Inference:
Membership of all Clusters
matstd_heart <- scale(heart)
set.seed(123)
kmeans2_heart <- kmeans(matstd_heart, centers = 2, nstart = 25)
kmeans2_heart
## K-means clustering with 2 clusters of sizes 586, 604
##
## Cluster means:
## age sex chest.pain.type resting.bp.s cholesterol
## 1 0.3477414 0.2946989 0.5082074 0.1895076 -0.2523240
## 2 -0.3373783 -0.2859165 -0.4930621 -0.1838600 0.2448045
## fasting.blood.sugar resting.ecg max.heart.rate exercise.angina oldpeak
## 1 0.2328022 0.05839825 -0.5566254 0.6477281 0.5274243
## 2 -0.2258643 -0.05665790 0.5400372 -0.6284249 -0.5117064
## ST.slope target
## 1 0.6293011 0.7936502
## 2 -0.6105471 -0.7699984
##
## Clustering vector:
## [1] 2 2 2 1 2 2 2 2 1 2 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 2 2 2 1 1 2 2 1
## [38] 2 2 1 2 1 2 2 1 1 2 2 2 2 1 1 2 2 1 2 1 1 2 1 2 2 2 1 2 2 2 2 1 2 1 2 1 2
## [75] 1 2 2 2 2 2 2 2 1 2 1 1 1 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2 1 1 1 2 2 2 2 2 2
## [112] 1 2 2 2 1 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 1 1 1 1 2 2 2 1 1 1 1 1 2 2 2 2 2
## [149] 2 1 2 2 2 2 2 1 1 2 1 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 1 1 1 2 2 2 1 2 1 1
## [186] 2 1 2 1 1 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 1 2 2 2 2 2 1
## [223] 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2 1 2 1 1 2 1 1 2 1 2 1 1 1 1 2 1 2 2 1 2 2 2
## [260] 2 2 2 2 1 1 1 2 1 2 1 2 2 2 1 2 2 2 1 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2
## [297] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 1 1 1
## [334] 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [408] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1
## [445] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 2 1 2 1 1 1 1 2 1 2 1 1 1
## [482] 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 2 1 1 1 2
## [519] 1 1 1 2 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1 2 1 2 1 1
## [556] 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2
## [593] 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 2 2 1 1 1 1 2 1
## [630] 2 1 2 2 1 1 2 2 1 2 2 2 2 2 2 2 1 2 1 2 2 1 1 1 1 2 2 2 2 2 2 2 1 2 2 2 1
## [667] 1 1 2 2 2 2 2 1 2 1 1 2 1 2 2 1 1 2 2 2 2 1 2 2 2 2 1 1 2 2 2 1 1 1 2 1 2
## [704] 2 1 2 1 2 2 1 1 2 1 2 2 2 2 2 1 2 1 1 2 2 1 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1
## [741] 2 2 2 1 2 2 1 1 1 2 1 2 1 2 1 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 1 2 2 1
## [778] 1 1 2 1 2 2 2 1 2 2 2 1 1 2 2 1 1 1 1 2 2 1 2 2 2 2 1 2 2 1 2 1 2 2 2 2 2
## [815] 2 2 1 2 2 1 1 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 1 1 2 1 2 2 1 1 2 2 1 1 2 1
## [852] 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 1 1 2 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 1 1
## [889] 1 1 2 2 2 1 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 1 2 1 2 1 2 2 2 2 1 1
## [926] 1 1 1 2 2 2 2 1 2 1 2 1 2 2 2 2 1 1 2 2 2 2 1 1 1 2 1 1 1 2 1 1 2 1 1 2 2
## [963] 2 1 2 2 1 1 2 2 1 2 2 2 2 2 2 2 1 2 2 2 1 1 1 2 2 2 2 2 2 1 2 1 1 1 1 1 1
## [1000] 2 1 1 2 2 2 1 1 1 1 2 1 2 2 1 1 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 1 2 2 1 2 2
## [1037] 2 2 2 2 1 1 1 1 2 1 2 2 1 2 2 2 2 2 2 2 2 1 1 1 2 1 1 2 1 2 2 2 1 2 1 2 2
## [1074] 2 1 2 1 2 1 1 1 2 1 2 2 2 2 2 2 2 2 2 1 1 1 2 1 2 1 2 1 2 2 2 2 2 2 2 2 2
## [1111] 1 1 2 2 2 1 1 2 1 2 2 2 1 1 2 2 2 2 2 2 1 2 1 2 1 2 2 1 1 1 2 2 2 2 2 2 2
## [1148] 2 2 2 2 1 1 1 1 2 2 1 2 1 2 2 2 2 2 2 2 1 2 1 2 2 1 1 2 2 2 1 2 1 1 1 2 1
## [1185] 1 2 1 1 2 2
##
## Within cluster sum of squares by cluster:
## [1] 5913.854 5286.896
## (between_SS / total_SS = 21.5 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
km.res <- kmeans(matstd_heart, 2, nstart = 25)
# Visualize
fviz_cluster(km.res, data = matstd_heart,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
repel = TRUE)
Inference:
The application of hierarchical clustering and k-means clustering helped identify natural groupings within the data, indicating distinct patterns or profiles associated with the risk of heart disease. These clusters could represent different patient profiles based on their risk levels, guiding personalized medicine or targeted health interventions.
heart1 <- cor(heart)
heart1_pca <- prcomp(heart1,scale=TRUE)
summary(heart1_pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.3294 1.2997 1.1715 0.98645 0.83304 0.78164 0.65754
## Proportion of Variance 0.4522 0.1408 0.1144 0.08109 0.05783 0.05091 0.03603
## Cumulative Proportion 0.4522 0.5929 0.7073 0.78838 0.84621 0.89713 0.93316
## PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.53926 0.46021 0.4242 0.34583 4.306e-17
## Proportion of Variance 0.02423 0.01765 0.0150 0.00997 0.000e+00
## Cumulative Proportion 0.95739 0.97504 0.9900 1.00000 1.000e+00
Inference:
Scree Plot
To further understand the ideal number of PCs, we can carry out the Scree Plot
#Eigenvalues represent the amount of variance explained by each principal component
#protein_pca$sdev contains the standard deviations of the principal components, and ^2 squares these values to obtain the eigenvalues. The results are stored in a variable named eigen_protein.
(eigen_heart1 <- heart1_pca$sdev^2)
## [1] 5.426052e+00 1.689157e+00 1.372310e+00 9.730747e-01 6.939582e-01
## [6] 6.109546e-01 4.323579e-01 2.908047e-01 2.117943e-01 1.799400e-01
## [11] 1.195964e-01 1.854463e-33
names(eigen_heart1) <- paste("PC",1:9,sep="")
plot(eigen_heart1, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")
fviz_eig(heart1_pca, addlabels = TRUE)
Inference:
Bi-Plot
#Generates a PCA variable plot where the variables are colored based on their quality of representation on the principal components
fviz_pca_var(heart1_pca,col.var = "cos2",
gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
repel = TRUE)
Inference:
Individual PCA
#PCA is conducted and results are stored in res.pca
res.pca <- PCA(heart, graph = FALSE)
#Individuals (samples or observations) in the PCA space are visualized using fviz_pca_ind()
fviz_pca_ind(res.pca)
fviz_pca_biplot(res.pca, repel = TRUE,
col.var = "#FC4E07", # Variables color
)
Inference:
fa.parallel(heart)
## Parallel analysis suggests that the number of factors = 5 and the number of components = 3
Inference:
Factor Model
fit.pc <- principal(heart, nfactors=2, rotate="varimax")
round(fit.pc$values, 3)
## [1] 3.321 1.501 1.198 0.963 0.887 0.862 0.769 0.632 0.556 0.502 0.425 0.383
fit.pc$loadings
##
## Loadings:
## RC1 RC2
## age 0.423 0.380
## sex 0.425 -0.335
## chest.pain.type 0.603
## resting.bp.s 0.154 0.488
## cholesterol -0.371 0.632
## fasting.blood.sugar 0.330 -0.193
## resting.ecg 0.543
## max.heart.rate -0.674
## exercise.angina 0.661 0.194
## oldpeak 0.519 0.485
## ST.slope 0.670 0.257
## target 0.804
##
## RC1 RC2
## SS loadings 3.251 1.572
## Proportion Var 0.271 0.131
## Cumulative Var 0.271 0.402
Inference:
fit.pc$communality
## age sex chest.pain.type resting.bp.s
## 0.3237603 0.2928463 0.3637780 0.2615261
## cholesterol fasting.blood.sugar resting.ecg max.heart.rate
## 0.5371617 0.1463153 0.2951713 0.4585609
## exercise.angina oldpeak ST.slope target
## 0.4745965 0.5045918 0.5150005 0.6494190
Inference:
Visualizing the Columns that go into each Factor
fa.diagram(fit.pc)
Inference:
Multiple Regression
# Load mtcars dataset
head(heart)
## age sex chest.pain.type resting.bp.s cholesterol fasting.blood.sugar
## 1 40 1 2 140 289 0
## 2 49 0 3 160 180 0
## 3 37 1 2 130 283 0
## 4 48 0 4 138 214 0
## 5 54 1 3 150 195 0
## 6 39 1 3 120 339 0
## resting.ecg max.heart.rate exercise.angina oldpeak ST.slope target
## 1 0 172 0 0.0 1 0
## 2 0 156 0 1.0 2 1
## 3 1 98 0 0.0 1 0
## 4 0 108 1 1.5 2 1
## 5 0 122 0 0.0 1 0
## 6 0 170 0 0.0 1 0
names(heart)
## [1] "age" "sex" "chest.pain.type"
## [4] "resting.bp.s" "cholesterol" "fasting.blood.sugar"
## [7] "resting.ecg" "max.heart.rate" "exercise.angina"
## [10] "oldpeak" "ST.slope" "target"
# Fitting the model
fit <- lm(max.heart.rate ~ age + sex + cholesterol + resting.bp.s, data = heart)
# Summary of the model to view results
summary(fit)
##
## Call:
## lm(formula = max.heart.rate ~ age + sex + cholesterol + resting.bp.s,
## data = heart)
##
## Residuals:
## Min 1Q Median 3Q Max
## -76.988 -15.874 1.762 17.266 56.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 192.541716 5.784639 33.285 < 2e-16 ***
## age -0.952521 0.073371 -12.982 < 2e-16 ***
## sex -8.154767 1.592202 -5.122 3.53e-07 ***
## cholesterol 0.049472 0.006721 7.361 3.41e-13 ***
## resting.bp.s -0.044020 0.037527 -1.173 0.241
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.81 on 1185 degrees of freedom
## Multiple R-squared: 0.2035, Adjusted R-squared: 0.2008
## F-statistic: 75.69 on 4 and 1185 DF, p-value: < 2.2e-16
coefficients(fit)
## (Intercept) age sex cholesterol resting.bp.s
## 192.54171586 -0.95252147 -8.15476720 0.04947247 -0.04401996
library(GGally)
ggpairs(data=heart, title="Heart_disease")
confint(fit,level=0.95)
## 2.5 % 97.5 %
## (Intercept) 181.1924399 203.89099185
## age -1.0964736 -0.80856933
## sex -11.2786163 -5.03091812
## cholesterol 0.0362862 0.06265874
## resting.bp.s -0.1176474 0.02960749
fitted(fit)
## 1 2 3 4 5 6 7 8
## 154.4208 147.7300 157.4218 151.3330 135.9949 158.7274 155.6806 138.3989
## 9 10 11 12 13 14 15 16
## 153.2217 155.5885 162.0145 131.2675 152.0486 143.1272 157.9122 149.3291
## 17 18 19 20 21 22 23 24
## 153.0455 156.2449 135.1028 158.0229 158.2137 146.2965 150.3537 150.1211
## 25 26 27 28 29 30 31 32
## 151.2001 154.7133 141.3077 143.6236 160.2369 139.6067 153.1472 133.5851
## 33 34 35 36 37 38 39 40
## 138.5301 148.1202 154.1822 160.9698 131.4488 161.0143 150.2949 151.4479
## 41 42 43 44 45 46 47 48
## 145.8812 149.9279 157.5064 141.5064 146.8038 138.1978 154.8936 141.2841
## 49 50 51 52 53 54 55 56
## 161.9866 154.7889 142.5654 152.6327 146.4425 159.8865 146.1930 146.5176
## 57 58 59 60 61 62 63 64
## 162.9340 133.9557 144.4052 146.8452 145.8279 157.5463 146.4425 148.9924
## 65 66 67 68 69 70 71 72
## 150.0669 164.8789 158.5609 160.1954 139.9829 156.2557 137.0406 147.3900
## 73 74 75 76 77 78 79 80
## 138.5774 156.1334 139.0941 142.0320 174.8828 161.3026 133.6403 142.1821
## 81 82 83 84 85 86 87 88
## 140.8599 139.4428 128.8075 137.5092 134.9804 122.2344 128.0009 146.5813
## 89 90 91 92 93 94 95 96
## 152.5426 137.1647 151.3162 156.7041 148.1174 147.8992 159.5552 136.4294
## 97 98 99 100 101 102 103 104
## 147.4185 147.4679 129.9685 153.1392 130.3554 138.9413 167.2311 164.0579
## 105 106 107 108 109 110 111 112
## 144.5785 136.7933 154.1043 155.9853 136.9800 150.7977 139.9212 136.1057
## 113 114 115 116 117 118 119 120
## 147.1100 156.7217 150.3864 168.8767 156.8600 147.3421 161.8367 153.5561
## 121 122 123 124 125 126 127 128
## 154.0997 150.9646 147.6022 148.8146 134.7968 139.8386 162.3985 150.1305
## 129 130 131 132 133 134 135 136
## 147.2018 150.3784 156.2542 145.7222 142.7577 135.8214 143.2602 145.7613
## 137 138 139 140 141 142 143 144
## 156.9375 153.8791 135.0004 149.0452 144.1880 147.4682 146.9717 139.7623
## 145 146 147 148 149 150 151 152
## 147.7209 155.9024 148.8942 158.6195 139.7899 157.0601 152.1526 142.1300
## 153 154 155 156 157 158 159 160
## 154.1684 140.0734 154.4477 141.1422 152.7487 140.7030 151.1004 135.5547
## 161 162 163 164 165 166 167 168
## 135.0861 142.5670 145.5865 151.3162 148.7953 147.9791 147.8647 142.0262
## 169 170 171 172 173 174 175 176
## 144.2776 134.1809 131.8335 163.5032 151.7493 143.5717 140.8020 141.8527
## 177 178 179 180 181 182 183 184
## 151.5138 137.4740 136.2240 153.0187 154.7776 140.2645 141.1676 148.6799
## 185 186 187 188 189 190 191 192
## 147.5032 149.4978 132.5362 135.8357 151.7761 155.8602 140.0794 146.4997
## 193 194 195 196 197 198 199 200
## 139.6172 145.0641 145.0795 157.0888 135.9904 147.1243 151.0367 140.7911
## 201 202 203 204 205 206 207 208
## 147.7629 147.0949 146.6672 144.6103 169.4460 134.4261 140.7945 161.0038
## 209 210 211 212 213 214 215 216
## 158.9209 158.5241 138.1343 147.0111 153.0009 138.9776 144.3124 144.1962
## 217 218 219 220 221 222 223 224
## 168.2077 156.2487 138.4039 135.5321 163.6123 145.8313 151.9101 151.1854
## 225 226 227 228 229 230 231 232
## 162.4141 139.3808 143.4387 138.2680 149.9296 154.6456 160.1346 159.0049
## 233 234 235 236 237 238 239 240
## 154.4653 164.6684 152.7715 150.2298 151.8507 156.6739 140.4299 149.1855
## 241 242 243 244 245 246 247 248
## 141.1709 141.7434 133.9423 139.4010 159.4606 144.8813 136.1282 139.3934
## 249 250 251 252 253 254 255 256
## 146.9004 146.6354 148.8609 160.8243 146.2464 135.2266 132.5749 137.8845
## 257 258 259 260 261 262 263 264
## 150.3311 153.9226 151.4088 147.2546 150.6138 148.0131 146.7566 146.7167
## 265 266 267 268 269 270 271 272
## 128.6991 143.0038 140.9967 143.8760 158.5712 139.2005 153.6766 147.3724
## 273 274 275 276 277 278 279 280
## 167.2345 135.7794 137.5998 156.3490 130.8022 137.7813 138.4048 147.4913
## 281 282 283 284 285 286 287 288
## 147.8995 134.1235 142.0933 149.1245 152.3294 155.9294 148.5207 130.3862
## 289 290 291 292 293 294 295 296
## 137.5754 156.2036 153.0262 144.2624 154.3248 137.1847 117.4108 149.7244
## 297 298 299 300 301 302 303 304
## 121.6610 130.3780 125.2510 130.9662 134.7762 120.1925 125.8355 128.4008
## 305 306 307 308 309 310 311 312
## 128.2030 131.6265 138.6807 126.9360 128.1807 124.0784 125.9113 115.6500
## 313 314 315 316 317 318 319 320
## 121.7332 139.8311 146.9389 130.3817 107.5175 125.4711 124.8830 120.5605
## 321 322 323 324 325 326 327 328
## 113.2326 122.6857 119.9761 151.7238 120.2683 136.1690 139.7590 136.6813
## 329 330 331 332 333 334 335 336
## 122.6857 130.6739 121.5131 122.1734 125.9835 143.7891 142.1042 130.0858
## 337 338 339 340 341 342 343 344
## 120.0482 108.7622 117.7751 118.2153 127.3984 139.0265 118.5834 121.4409
## 345 346 347 348 349 350 351 352
## 129.1332 130.5260 112.7203 122.9058 133.6036 112.6322 145.2540 128.6209
## 353 354 355 356 357 358 359 360
## 137.2657 125.7634 123.4181 126.7159 114.1851 135.5087 128.6209 143.1288
## 361 362 363 364 365 366 367 368
## 129.2812 118.2874 132.5752 124.2227 125.7634 125.7634 122.7763 119.6801
## 369 370 371 372 373 374 375 376
## 113.6728 123.9304 117.7751 121.2930 114.9175 116.2344 122.2455 120.7806
## 377 378 379 380 381 382 383 384
## 115.9645 132.7953 115.4299 111.5477 131.4785 120.1925 131.6986 138.3662
## 385 386 387 388 389 390 391 392
## 151.5037 127.6684 119.6801 137.9982 128.1807 125.8355 119.2399 129.6456
## 393 394 395 396 397 398 399 400
## 112.6482 120.5605 141.5881 123.0500 142.2484 127.3226 121.6573 127.5925
## 401 402 403 404 405 406 407 408
## 117.4791 137.8724 130.0858 116.0902 128.9131 134.7762 145.7663 123.9304
## 409 410 411 412 413 414 415 416
## 120.2683 123.3460 126.8601 118.7276 125.0272 125.5433 125.5433 127.2282
## 417 418 419 420 421 422 423 424
## 122.8522 131.0781 147.0932 132.2100 137.0272 127.2160 116.2381 127.5456
## 425 426 427 428 429 430 431 432
## 119.3121 121.9533 133.4016 133.7117 122.0254 120.4884 118.5234 124.4587
## 433 434 435 436 437 438 439 440
## 130.9322 125.6513 147.4043 118.8316 120.5446 124.0344 118.1432 118.6555
## 441 442 443 444 445 446 447 448
## 107.8256 129.2213 112.9404 130.1738 130.7149 130.7106 137.2913 127.2282
## 449 450 451 452 453 454 455 456
## 114.0441 128.7136 131.9983 129.4854 117.0867 134.9746 121.9533 133.1969
## 457 458 459 460 461 462 463 464
## 121.4091 121.0007 140.7836 120.3845 140.7555 137.6783 118.3914 134.3448
## 465 466 467 468 469 470 471 472
## 130.1738 122.4216 150.3558 126.7159 126.7222 126.2089 136.6691 128.3568
## 473 474 475 476 477 478 479 480
## 113.5407 127.1242 136.6621 119.5640 120.3526 140.7827 121.4409 139.7566
## 481 482 483 484 485 486 487 488
## 123.5624 123.5942 112.5002 127.6747 123.8583 116.5744 128.9948 137.7432
## 489 490 491 492 493 494 495 496
## 134.5175 128.7773 137.8480 121.1101 115.5074 131.9908 146.5488 131.6709
## 497 498 499 500 501 502 503 504
## 138.9839 145.9885 131.7791 132.5222 134.0812 128.7555 133.8930 122.7904
## 505 506 507 508 509 510 511 512
## 141.2280 128.7647 138.1323 118.0924 153.4934 115.2856 134.0941 130.8961
## 513 514 515 516 517 518 519 520
## 130.5441 153.5993 133.1643 138.0581 118.6555 122.6596 127.4961 134.1759
## 521 522 523 524 525 526 527 528
## 135.2413 128.7353 134.9520 147.6879 130.6453 133.3109 147.4764 131.5696
## 529 530 531 532 533 534 535 536
## 134.1651 138.9719 119.9492 141.6912 132.2693 136.0938 132.0030 133.6686
## 537 538 539 540 541 542 543 544
## 125.3232 119.4760 120.0613 137.2216 134.9971 129.3482 113.0076 148.5863
## 545 546 547 548 549 550 551 552
## 119.7258 143.0179 146.3118 143.7392 129.9268 129.5026 122.4512 137.2897
## 553 554 555 556 557 558 559 560
## 130.9322 121.3525 118.2035 135.7379 133.3722 121.2411 135.3053 134.5876
## 561 562 563 564 565 566 567 568
## 131.0329 137.1390 136.1441 135.5808 136.1480 137.1119 134.5223 147.1904
## 569 570 571 572 573 574 575 576
## 121.9687 157.6465 135.7786 136.4436 117.9421 126.3708 114.8473 122.8014
## 577 578 579 580 581 582 583 584
## 138.9662 127.6222 132.3964 131.7848 126.5776 137.5616 142.7934 123.9786
## 585 586 587 588 589 590 591 592
## 125.8192 129.2900 136.2693 140.4666 155.8227 125.2397 119.4625 126.5543
## 593 594 595 596 597 598 599 600
## 135.2763 132.1179 130.4669 134.7625 130.7149 137.7835 135.2960 137.8967
## 601 602 603 604 605 606 607 608
## 135.3661 134.6114 134.1705 137.6730 133.3722 122.4137 126.2828 151.7087
## 609 610 611 612 613 614 615 616
## 130.8534 142.4062 126.7858 150.0088 151.9894 126.2646 137.6602 142.0248
## 617 618 619 620 621 622 623 624
## 132.6142 127.9180 151.5630 137.5471 130.8023 130.0808 125.9473 137.9881
## 625 626 627 628 629 630 631 632
## 135.1699 135.5683 146.0652 133.8220 138.8333 147.9392 131.9610 147.6036
## 633 634 635 636 637 638 639 640
## 127.3539 149.7941 137.7834 129.0221 149.9683 126.6148 145.0641 153.3564
## 641 642 643 644 645 646 647 648
## 144.7806 149.5430 154.7030 154.6728 153.2751 135.5891 133.1807 135.7879
## 649 650 651 652 653 654 655 656
## 125.7571 162.6526 136.8328 140.3165 145.6083 130.3611 134.6510 147.5635
## 657 658 659 660 661 662 663 664
## 144.2784 150.6274 138.3667 148.2805 145.8710 133.4267 133.4166 139.8904
## 665 666 667 668 669 670 671 672
## 147.3799 126.6476 135.1561 153.9782 139.3631 145.0950 136.0172 155.5322
## 673 674 675 676 677 678 679 680
## 158.6618 128.4208 138.9141 141.0021 133.9500 129.7238 153.3296 148.3744
## 681 682 683 684 685 686 687 688
## 140.6608 129.5223 137.1446 142.5579 147.0905 157.4088 146.8861 133.8636
## 689 690 691 692 693 694 695 696
## 150.4789 122.9641 123.7334 135.0890 150.5596 147.2357 161.1005 157.5932
## 697 698 699 700 701 702 703 704
## 137.4389 133.4988 155.5619 135.8953 150.1981 135.1950 149.9374 129.9863
## 705 706 707 708 709 710 711 712
## 133.7102 163.0804 142.1797 132.9588 145.0412 140.6520 138.2999 139.8415
## 713 714 715 716 717 718 719 720
## 148.3812 131.1788 136.3153 140.9024 151.7045 152.8522 127.0106 153.4537
## 721 722 723 724 725 726 727 728
## 137.1275 131.2215 146.7629 142.3892 141.5513 130.7820 152.6636 148.4069
## 729 730 731 732 733 734 735 736
## 152.1174 143.5244 150.2025 153.6930 153.3765 147.6072 144.6446 134.2531
## 737 738 739 740 741 742 743 744
## 139.3239 141.7318 141.7295 136.9576 141.3947 140.9543 144.0063 133.2574
## 745 746 747 748 749 750 751 752
## 146.7205 138.9011 133.4640 141.0868 127.0785 149.3990 130.3134 137.8254
## 753 754 755 756 757 758 759 760
## 151.2315 135.7356 137.8619 165.3508 134.5234 127.5308 135.5205 142.1252
## 761 762 763 764 765 766 767 768
## 140.8435 138.4997 142.4401 141.3043 149.7058 134.4119 161.8167 152.7715
## 769 770 771 772 773 774 775 776
## 150.4677 149.5606 140.8479 150.9055 154.1960 136.5710 151.1264 135.3115
## 777 778 779 780 781 782 783 784
## 133.1195 154.3369 138.9537 139.2375 136.3195 149.0250 139.7353 152.6395
## 785 786 787 788 789 790 791 792
## 137.9268 155.2790 130.3495 123.1963 125.0662 130.9583 132.9266 155.8109
## 793 794 795 796 797 798 799 800
## 141.9555 144.3884 145.3961 127.6315 140.7789 150.9720 153.5361 149.0006
## 801 802 803 804 805 806 807 808
## 161.1560 140.3509 153.2898 134.3380 141.6288 146.8147 123.9753 138.6119
## 809 810 811 812 813 814 815 816
## 119.9358 143.4836 159.4534 145.8229 146.5785 145.1626 146.8505 132.4789
## 817 818 819 820 821 822 823 824
## 120.5799 128.1250 138.4800 134.4971 144.4378 139.2526 142.9076 146.6326
## 825 826 827 828 829 830 831 832
## 136.3920 133.2101 155.7892 134.9529 142.4266 156.7505 134.1922 161.1336
## 833 834 835 836 837 838 839 840
## 157.8581 139.0572 142.9007 140.4323 148.0776 139.9325 129.0964 131.8016
## 841 842 843 844 845 846 847 848
## 134.9814 162.1822 149.4338 140.7741 162.6428 144.6932 138.8634 143.2431
## 849 850 851 852 853 854 855 856
## 152.8787 149.3240 141.8368 131.0362 134.5557 147.5599 146.9028 146.2581
## 857 858 859 860 861 862 863 864
## 145.6520 125.2474 156.9565 149.3962 140.5812 153.0378 134.0296 129.9000
## 865 866 867 868 869 870 871 872
## 137.1128 130.2253 134.8040 136.9692 147.5879 151.8928 139.6238 132.0734
## 873 874 875 876 877 878 879 880
## 132.8102 131.7020 143.6514 133.8361 149.0452 148.8337 131.7044 137.9085
## 881 882 883 884 885 886 887 888
## 145.1505 145.1529 137.1294 150.2049 147.5826 133.4291 127.6739 129.5223
## 889 890 891 892 893 894 895 896
## 127.6739 126.6148 155.7892 157.8581 137.4389 140.5812 150.4789 131.2215
## 897 898 899 900 901 902 903 904
## 137.7834 133.4291 147.5826 137.9881 150.2049 137.1294 131.8016 145.1529
## 905 906 907 908 909 910 911 912
## 138.6119 154.7030 145.1505 129.0221 144.6932 137.9085 134.4119 131.7044
## 913 914 915 916 917 918 919 920
## 150.4677 148.8337 134.2531 149.0452 149.7058 132.4789 133.4640 133.8361
## 921 922 923 924 925 926 927 928
## 133.8220 148.2805 149.3990 146.9028 137.1446 143.6514 131.7020 135.1561
## 929 930 931 932 933 934 935 936
## 149.9683 132.8102 132.0734 145.0412 135.5891 139.6238 142.1797 145.0950
## 937 938 939 940 941 942 943 944
## 137.9268 158.6618 125.9473 151.8928 147.5879 134.0296 140.6520 142.1252
## 945 946 947 948 949 950 951 952
## 149.0006 140.9543 140.8435 153.3296 151.2315 134.1922 150.2025 136.9692
## 953 954 955 956 957 958 959 960
## 134.8040 130.2253 137.8254 136.8328 145.3961 137.1128 127.6315 133.2574
## 961 962 963 964 965 966 967 968
## 129.9000 147.3799 141.3947 134.4971 153.0378 145.0641 135.8953 147.2357
## 969 970 971 972 973 974 975 976
## 149.3962 156.9565 125.2474 145.6520 147.9392 146.2581 147.1096 147.5599
## 977 978 979 980 981 982 983 984
## 150.9055 131.1788 134.5557 131.0362 152.8522 139.0572 141.8368 135.1699
## 985 986 987 988 989 990 991 992
## 141.5513 138.9011 144.2784 149.3240 155.8109 147.6036 133.1807 141.7318
## 993 994 995 996 997 998 999 1000
## 143.4836 130.7820 135.7879 133.8636 152.8787 143.2431 137.8619 138.8634
## 1001 1002 1003 1004 1005 1006 1007 1008
## 162.6428 140.7741 149.4338 133.4166 162.1822 134.9814 129.0964 145.6083
## 1009 1010 1011 1012 1013 1014 1015 1016
## 146.0652 142.3892 136.5710 130.3495 155.5322 144.6446 139.9325 148.0776
## 1017 1018 1019 1020 1021 1022 1023 1024
## 138.3667 140.4323 142.9007 161.1336 142.5579 156.7505 146.5785 119.9358
## 1025 1026 1027 1028 1029 1030 1031 1032
## 133.9500 155.5619 142.4266 132.9588 134.9529 139.3631 133.2101 136.3920
## 1033 1034 1035 1036 1037 1038 1039 1040
## 146.8861 137.1275 152.7715 151.1264 146.6326 142.9076 161.1560 151.5630
## 1041 1042 1043 1044 1045 1046 1047 1048
## 139.2526 130.3134 127.9180 144.4378 138.4800 135.5683 128.1250 145.8710
## 1049 1050 1051 1052 1053 1054 1055 1056
## 120.5799 146.8505 145.1626 145.8229 134.5234 139.8134 149.5430 159.4534
## 1057 1058 1059 1060 1061 1062 1063 1064
## 152.6636 123.9753 138.8333 141.0021 146.8147 127.5308 136.9576 141.6288
## 1065 1066 1067 1068 1069 1070 1071 1072
## 134.3380 153.2898 140.3509 146.7629 153.5361 149.9374 133.7102 143.5244
## 1073 1074 1075 1076 1077 1078 1079 1080
## 136.0172 150.9720 126.6476 138.4997 125.0662 140.7789 144.3884 149.8376
## 1081 1082 1083 1084 1085 1086 1087 1088
## 141.9555 132.9266 130.9583 123.1963 155.2790 151.7045 134.6510 152.6395
## 1089 1090 1091 1092 1093 1094 1095 1096
## 139.7353 129.7238 140.9024 149.0250 150.5596 136.3195 140.3165 139.2375
## 1097 1098 1099 1100 1101 1102 1103 1104
## 138.9537 162.6526 154.3369 150.1981 133.1195 141.3043 135.3115 154.1960
## 1105 1106 1107 1108 1109 1110 1111 1112
## 154.6728 140.8479 135.5205 161.8167 149.5606 161.1005 142.4401 141.0868
## 1113 1114 1115 1116 1117 1118 1119 1120
## 165.3508 144.7806 135.7356 138.2999 127.0785 146.7205 148.4069 139.8904
## 1121 1122 1123 1124 1125 1126 1127 1128
## 130.0808 144.0063 141.7295 139.3239 147.6072 153.3765 153.6930 152.1174
## 1129 1130 1131 1132 1133 1134 1135 1136
## 163.0804 153.4537 131.9610 138.9141 127.0106 136.3153 148.3812 139.8415
## 1137 1138 1139 1140 1141 1142 1143 1144
## 129.9863 135.1950 133.4988 130.8023 153.2751 153.3564 157.5932 135.0890
## 1145 1146 1147 1148 1149 1150 1151 1152
## 123.7334 122.9641 137.5471 157.4088 147.0905 140.6608 148.3744 128.4208
## 1153 1154 1155 1156 1157 1158 1159 1160
## 153.9782 139.3137 133.4267 150.6274 147.5635 130.3611 125.7571 149.7941
## 1161 1162 1163 1164 1165 1166 1167 1168
## 127.3539 132.3819 127.1724 137.0017 160.2026 134.7918 141.3190 141.8243
## 1169 1170 1171 1172 1173 1174 1175 1176
## 146.4124 144.6603 155.1770 129.8111 139.8547 140.9434 134.5222 136.2566
## 1177 1178 1179 1180 1181 1182 1183 1184
## 137.6367 124.3651 151.2620 145.5545 127.4667 136.8205 147.8184 129.6761
## 1185 1186 1187 1188 1189 1190
## 144.0081 149.7420 122.8248 130.8515 144.2009 150.7741
#showing error in each of the prediction
residuals(fit)
## 1 2 3 4 5 6
## 17.57915980 8.26998469 -59.42176938 -43.33304000 -13.99492744 11.27261546
## 7 8 9 10 11 12
## 14.31936901 3.60113203 -23.22166179 -35.58847242 -20.01451848 -32.26747429
## 13 14 15 16 17 18
## -7.04860061 -3.12716088 -20.91221050 0.67085364 12.95445811 8.75513551
## 19 20 21 22 23 24
## -10.10283766 1.97706913 -16.21365810 -4.29654376 13.64634420 -0.12108223
## 25 26 27 28 29 30
## -13.20007675 23.28667219 -29.30767864 -25.62361932 -33.23693990 5.39331646
## 31 32 33 34 35 36
## -23.14715768 -19.58505442 -16.53012816 -18.12023891 -0.18217860 -5.96977482
## 37 38 39 40 41 42
## -44.44883538 -19.01425824 -2.29491775 -21.44794264 -15.88123121 -49.92786871
## 43 44 45 46 47 48
## 10.49356386 28.49359171 -26.80381298 -18.19783350 13.10637944 28.71586512
## 49 50 51 52 53 54
## 22.01341888 15.21108249 -21.56536652 -54.63266848 -24.44252204 -9.88649668
## 55 56 57 58 59 60
## -6.19304967 23.48241301 -9.93395567 6.04425475 -10.40524795 -50.84518247
## 61 62 63 64 65 66
## 28.17206374 17.45369320 -2.44252204 -23.99244086 -5.06688623 -34.87886928
## 67 68 69 70 71 72
## -14.56093949 23.80462753 -57.98286695 13.74433104 7.95936424 -12.38999085
## 73 74 75 76 77 78
## 11.42257298 -41.13337506 -11.09409613 -26.03198008 -44.88284477 -11.30257300
## 79 80 81 82 83 84
## 4.35971501 27.81786879 19.14005282 14.55715741 -13.80746342 27.49075673
## 85 86 87 88 89 90
## -9.98038901 -28.23441081 -16.00092023 -4.58133765 2.45738009 -27.16466966
## 91 92 93 94 95 96
## 8.68375745 -16.70406579 -0.11742348 -55.89916815 20.44482702 3.57063107
## 97 98 99 100 101 102
## -9.41849302 12.53212876 10.03148882 -9.13916864 -15.35538829 -38.94133148
## 103 104 105 106 107 108
## -37.23107258 -12.05786721 -20.57848568 3.20672661 -44.10429821 12.01466607
## 109 110 111 112 113 114
## -1.98002968 -44.79768497 -15.92117914 -44.10571143 -22.11004772 -6.72166294
## 115 116 117 118 119 120
## -15.38637088 -18.87673974 13.14002498 -17.34205018 23.16333513 26.44386994
## 121 122 123 124 125 126
## 15.90031455 -11.96461704 -7.60215893 -38.81455972 15.20322270 -29.83862238
## 127 128 129 130 131 132
## 27.60154078 24.86945737 -7.20183000 1.62162445 -26.25420077 4.27779507
## 133 134 135 136 137 138
## -20.75767270 -11.82142106 -23.26021839 29.23869345 18.06252088 -7.87908213
## 139 140 141 142 143 144
## -17.00042530 -19.04523229 -50.18802720 -22.46819408 11.02826437 15.23767276
## 145 146 147 148 149 150
## 2.27906175 -23.90240088 6.10579866 17.38045678 20.21014466 -32.06009585
## 151 152 153 154 155 156
## -32.15259822 -42.13004521 -4.16842516 -0.07344027 5.55233714 8.85776169
## 157 158 159 160 161 162
## -2.74870705 -10.70300967 -51.10042637 -5.55472784 -16.08612034 -46.56700597
## 163 164 165 166 167 168
## 28.41349363 8.68375745 1.20474360 -7.97911139 27.13532070 -2.02622198
## 169 170 171 172 173 174
## -26.27757225 -34.18089772 28.16651844 -3.50324183 36.25067337 18.42829229
## 175 176 177 178 179 180
## 31.19804538 -7.85271561 -16.51380330 -32.47404898 13.77601277 -3.01871923
## 181 182 183 184 185 186
## -64.77758199 -20.26454379 8.83240721 -24.67991696 -7.50321398 -19.49777445
## 187 188 189 190 191 192
## -40.53620152 -25.83569925 -13.77614929 -45.86021831 -20.07937275 -26.49966071
## 193 194 195 196 197 198
## -23.61722878 14.93592084 -35.07950268 22.91122441 -19.99037830 -15.12432590
## 199 200 201 202 203 204
## -15.03667571 -24.79114385 -49.76291892 2.90511028 3.33276540 1.38969319
## 205 206 207 208 209 210
## -19.44602590 -34.42608647 -0.79446281 18.99617624 -18.92092720 26.47588086
## 211 212 213 214 215 216
## 1.86565163 -37.01106271 -13.00092018 -10.97755404 19.68760976 -46.19622444
## 217 218 219 220 221 222
## 1.79234526 -6.24870820 -1.40392064 14.46792197 6.38770789 -33.83125521
## 223 224 225 226 227 228
## -1.91008661 -26.18542227 22.58585802 -2.38082564 6.56128619 1.73195230
## 229 230 231 232 233 234
## -15.92957575 15.35444724 23.86543552 -1.00488853 12.53473999 -35.66843491
## 235 236 237 238 239 240
## -10.77145112 -10.22975622 8.14928929 -38.67392417 -4.42985292 -50.18545247
## 241 242 243 244 245 246
## -39.17091175 13.25660020 8.05765312 3.59896369 -41.46057527 -41.88134726
## 247 248 249 250 251 252
## 0.87181314 10.60662989 3.09958696 -16.63535927 -28.86091515 -25.82429376
## 253 254 255 256 257 258
## -31.24636586 -20.22660604 19.42513677 -41.88454686 -20.33114031 -3.92259460
## 259 260 261 262 263 264
## 20.59122259 -27.25462143 4.38620877 16.98690328 -8.75657774 -31.71670707
## 265 266 267 268 269 270
## -3.69911858 1.99616759 34.00330006 -33.87603436 -8.57120667 -48.20053289
## 271 272 273 274 275 276
## -8.67664310 -7.37239370 -2.23448268 -5.77944040 -3.59981659 23.65096351
## 277 278 279 280 281 282
## -30.80222580 12.21874532 -12.40480046 -21.49134741 7.10050270 0.87650647
## 283 284 285 286 287 288
## -20.09329160 10.87552991 7.67062989 14.07060207 -28.52069507 9.61376465
## 289 290 291 292 293 294
## -5.57543307 -0.20355231 26.97378896 -6.26241425 -19.32483792 10.81529405
## 295 296 297 298 299 300
## -24.41075745 -22.72436531 -11.66104294 8.62201921 5.74897096 -38.96615789
## 301 302 303 304 305 306
## 14.22375621 28.80753336 24.16452679 -8.40081555 -5.20298927 -5.62645729
## 307 308 309 310 311 312
## -11.68072550 28.06402780 -8.18071575 13.92159223 56.08867156 38.35004093
## 313 314 315 316 317 318
## -11.73316523 36.16892675 7.06107683 10.61828627 15.48253461 22.52887116
## 319 320 321 322 323 324
## -3.88295173 -43.56054395 22.76740576 52.31431330 -10.97609979 14.27619594
## 325 326 327 328 329 330
## 7.73167813 -3.16896486 -11.75895097 1.31871326 -3.68568670 -48.67393581
## 331 332 333 334 335 336
## 8.48693457 20.82663518 -43.98345072 35.21086334 1.89580649 39.91424130
## 337 338 339 340 341 342
## 13.95177792 5.23779105 36.22489818 30.78469859 17.60155469 -17.02652929
## 343 344 345 346 347 348
## -4.58337872 -8.44094314 -9.13323723 -26.52595830 17.27972764 -7.90578650
## 349 350 351 352 353 354
## -5.60362252 -8.63223244 -20.25398002 -8.62091535 2.73426909 -25.76335092
## 355 356 357 358 359 360
## -23.41810838 -34.71587240 10.81488429 -22.50866547 -33.62091535 -15.12883727
## 361 362 363 364 365 366
## -14.28121474 -46.28742370 -8.57524582 -25.22265234 22.23664908 -28.76335092
## 367 368 369 370 371 372
## 17.22365044 -2.68014476 6.32720617 -3.93043026 -31.77510182 -58.29296563
## 373 374 375 376 377 378
## -6.91753739 -18.23440323 -7.24548711 -15.78064375 5.03554533 -14.79534562
## 379 380 381 382 383 384
## 6.57014073 45.45234891 24.52152023 -21.19246664 -11.69857957 6.63377010
## 385 386 387 388 389 390
## 4.49629573 27.33160613 -14.68014476 -38.99815259 6.81928425 -42.83547321
## 391 392 393 394 395 396
## 25.76005483 -69.64555911 -20.64815007 -5.56054395 -21.58813869 -25.05003107
## 397 398 399 400 401 402
## 7.75156192 15.67740992 -16.65731000 -5.59253865 -47.47914679 -27.87244859
## 403 404 405 406 407 408
## 32.91424130 -49.09015866 -0.91313743 -14.77624379 -15.76630190 -23.93043026
## 409 410 411 412 413 414
## -48.26832187 -29.34598609 -4.86011697 -40.72762329 24.97280370 -22.54325113
## 415 416 417 418 419 420
## -27.54325113 -17.22819428 -32.85220479 -19.07814454 -20.09315601 7.78997525
## 421 422 423 424 425 426
## 11.97284273 -28.21597264 3.76186382 -22.54556263 20.68793255 19.04673498
## 427 428 429 430 431 432
## 23.59838291 6.28833822 -5.02538731 -0.48842167 1.47655887 23.54133023
## 433 434 435 436 437 438
## -44.93216626 -41.65133045 -22.40426903 1.16841916 -2.54462632 -0.03438781
## 439 440 441 442 443 444
## -12.14317913 -7.65550101 8.17439489 50.77872285 16.05962784 -5.17379862
## 445 446 447 448 449 450
## 9.28505448 -10.71059828 -13.29127702 -10.22819428 -4.04411310 -23.71357114
## 451 452 453 454 455 456
## 23.00173246 -19.48539691 4.91329990 -16.97463091 11.04673498 -10.19690076
## 457 458 459 460 461 462
## 9.59089212 -41.00074355 24.21640527 -34.38446412 -29.75549240 -19.67832540
## 463 464 465 466 467 468
## -34.39138125 -17.34483293 -23.17379862 5.57843305 9.64423420 -1.71587240
## 469 470 471 472 473 474
## 3.27777171 -29.20887183 24.33089483 -22.35679559 16.45926605 12.87576327
## 475 476 477 478 479 480
## -14.66214753 10.43599748 -0.35262885 -1.78271803 -13.44094314 8.24343086
## 481 482 483 484 485 486
## -0.56235295 -13.59418822 5.49982744 -2.67474346 -17.85830797 -4.57437822
## 487 488 489 490 491 492
## -0.99484814 42.25681866 9.48246039 6.22267820 2.15198129 -19.11011667
## 493 494 495 496 497 498
## -7.50735706 13.00919835 -19.54878753 -21.67088021 1.01609008 -76.98846136
## 499 500 501 502 503 504
## 16.22090926 -2.52224618 -4.08124734 11.24448825 4.10697713 17.20955293
## 505 506 507 508 509 510
## -3.22797029 -16.76468307 -7.13230908 -6.09243011 -73.49336762 34.71438530
## 511 512 513 514 515 516
## -24.09405734 -4.89607802 -42.54405267 -0.59931027 16.83572006 -18.05809018
## 517 518 519 520 521 522
## 41.34449899 9.34037321 -7.49609016 -24.17588199 -14.24128407 -0.73534114
## 523 524 525 526 527 528
## 0.04801890 -27.68789403 -13.64530244 16.68913061 -3.47639132 -18.56959038
## 529 530 531 532 533 534
## 0.83492566 -11.97187294 -10.94924018 -13.69121954 -17.26929697 -34.09383232
## 535 536 537 538 539 540
## 7.99703646 1.33142416 -3.32315133 -0.47596260 9.93873622 -25.22163394
## 541 542 543 544 545 546
## -34.99710634 -7.34824742 6.99236971 -43.58625956 9.27423277 -23.01790869
## 547 548 549 550 551 552
## -7.31179602 18.26077260 -29.92679916 10.49738854 12.54876829 -64.28967764
## 553 554 555 556 557 558
## -44.93216626 -13.35246643 -2.20351968 24.26210036 -15.37218090 -9.24111133
## 559 560 561 562 563 564
## -13.30528612 -10.58758253 -29.03288498 -0.13904654 4.85585545 18.41915493
## 565 566 567 568 569 570
## -10.14795762 22.88808171 -19.52228669 -19.19036725 -6.96874587 -52.64648193
## 571 572 573 574 575 576
## -25.77864071 -17.44355286 -8.94214465 8.62923226 15.15267680 -10.80135209
## 577 578 579 580 581 582
## -12.96624916 -7.62216335 -22.39643851 -12.78484884 -16.57761763 -7.56155473
## 583 584 585 586 587 588
## 16.20660196 -39.97858613 0.18082702 -13.29004353 -16.26928685 -18.46664659
## 589 590 591 592 593 594
## 9.17730747 -3.23968723 -25.46254143 6.44566061 -25.27634404 17.88205370
## 595 596 597 598 599 600
## -0.46687771 -21.76246283 9.28505448 -37.78352256 0.70397946 -10.89665143
## 601 602 603 604 605 606
## -37.36606347 -38.61143189 -11.17052686 -39.67296715 -15.37218090 -10.41373260
## 607 608 609 610 611 612
## 24.71717792 -55.70874344 -22.85343199 -14.40617840 11.21421588 -24.00875305
## 613 614 615 616 617 618
## 2.01064494 10.73540349 -37.66019409 -7.02481111 -39.61423037 -18.91798717
## 619 620 621 622 623 624
## 8.43704320 3.45293478 -25.80228000 -9.08082697 14.05271453 4.01189543
## 625 626 627 628 629 630
## 6.83009272 34.43169941 7.93483424 27.17795407 -27.83325527 32.06075927
## 631 632 633 634 635 636
## 13.03897706 11.39640353 -2.35385424 -29.79410577 17.21657170 14.97792935
## 637 638 639 640 641 642
## 28.03168242 2.38518885 34.93592084 27.64361061 -1.78058849 9.45700605
## 643 644 645 646 647 648
## -15.70302056 -2.67278468 3.72489479 29.41086343 -3.18070109 14.21213378
## 649 650 651 652 653 654
## 12.24293823 7.34739203 3.16718509 -14.31649546 4.39172363 7.63885361
## 655 656 657 658 659 660
## -9.65097341 2.43650278 41.72162806 30.37258257 24.63334358 30.71950463
## 661 662 663 664 665 666
## 10.12897780 0.57333402 31.58339929 -13.89043973 29.62011449 -6.64756630
## 667 668 669 670 671 672
## -21.15613262 -28.97816140 44.63686577 11.90495286 42.98279904 19.46778643
## 673 674 675 676 677 678
## 9.33821059 -3.42081489 -42.91413252 1.99787819 -30.94998715 43.27623766
## 679 680 681 682 683 684
## -11.32963035 20.62561235 30.33917290 20.47771204 -25.14463337 43.44212529
## 685 686 687 688 689 690
## 4.90952510 -8.40875435 5.11390521 6.13641332 12.52114770 20.03591224
## 691 692 693 694 695 696
## -7.73336673 6.91097706 -3.55964238 0.76431899 17.89947561 15.40683425
## 697 698 699 700 701 702
## 40.56114531 -28.49878827 -25.56185167 -24.89527706 17.80191720 -9.19499623
## 703 704 705 706 707 708
## 28.06262374 10.01366310 11.28980328 -0.08039741 -14.17969207 31.04119603
## 709 710 711 712 713 714
## 23.95877256 -31.65199201 -30.29992303 28.15849857 -30.38117403 19.82117680
## 715 716 717 718 719 720
## 19.68473402 -7.90243137 10.29546947 22.14776589 -56.01059094 9.54633575
## 721 722 723 724 725 726
## -13.12747614 15.77849070 19.23709935 0.61075338 15.44866838 31.21798487
## 727 728 729 730 731 732
## -14.66360980 -31.40694089 0.88259606 17.47562179 19.79750635 8.30696872
## 733 734 735 736 737 738
## 8.62347064 -3.60721160 -11.64459376 -20.25308362 -36.32386135 -2.73182628
## 739 740 741 742 743 744
## -25.72948140 -48.95764851 9.60528304 11.04572063 18.99367012 -34.25737252
## 745 746 747 748 749 750
## 22.27951051 19.09887542 26.53600617 27.91319729 4.92153975 28.60096859
## 751 752 753 754 755 756
## -34.31340763 27.17459104 8.76847841 36.26438162 6.13810295 26.64915006
## 757 758 759 760 761 762
## 33.47660803 4.46915546 46.47953243 20.87483307 -15.84349537 56.50033319
## 763 764 765 766 767 768
## -47.44009302 18.69573458 -35.70579721 38.58809746 10.18327716 26.22854888
## 769 770 771 772 773 774
## 7.53228131 17.43944897 -18.84790623 -1.90547914 17.80398312 -25.57099998
## 775 776 777 778 779 780
## 18.87355066 26.68846167 31.88053030 27.66312113 15.04632596 15.76253912
## 781 782 783 784 785 786
## -6.31951896 11.97497838 14.26469733 6.36054514 14.07320695 -3.27899884
## 787 788 789 790 791 792
## 43.65046407 7.80366781 20.93381915 -5.95828349 -17.92655235 18.18914652
## 793 794 795 796 797 798
## -35.95553724 -22.38835624 1.60389171 35.36847681 22.22109504 43.02795477
## 799 800 801 802 803 804
## -3.53608039 8.99936190 -39.15598354 32.64905574 8.71024032 -29.33804655
## 805 806 807 808 809 810
## 5.37123732 10.18525532 -11.97534729 21.38808413 5.06423831 12.51637227
## 811 812 813 814 815 816
## -3.45341969 29.17707635 14.42154140 -23.16264781 11.14952998 18.52113905
## 817 818 819 820 821 822
## 41.42006788 22.87499167 32.52004975 6.50293659 28.56217129 5.74738111
## 823 824 825 826 827 828
## 35.09240475 13.36736191 17.60799897 -2.21007367 31.21082225 24.04713908
## 829 830 831 832 833 834
## 23.57338547 8.24950575 -3.19220259 40.86638424 14.14187474 32.94276825
## 835 836 837 838 839 840
## 11.09927125 6.56770794 21.92244719 -13.93251466 -2.09636655 42.19839377
## 841 842 843 844 845 846
## -2.98141729 19.81782751 -17.43378579 -43.77405023 -26.64277128 17.30681359
## 847 848 849 850 851 852
## 51.13664317 2.75693885 -12.87872763 35.67596992 19.16324209 14.96383612
## 853 854 855 856 857 858
## 10.44432344 12.44011790 -26.90275792 9.74188936 26.34800926 24.75264658
## 859 860 861 862 863 864
## 25.04351917 -6.39621598 19.41878700 -11.03784817 9.97039875 28.09996931
## 865 866 867 868 869 870
## 10.88717834 24.77472655 7.19599641 -23.96921891 40.41211926 1.10721436
## 871 872 873 874 875 876
## -16.62384077 24.92664789 29.18981536 5.29804415 -11.65141606 24.16394141
## 877 878 879 880 881 882
## 21.95476771 23.16628381 0.29560501 22.09150953 25.84952037 22.84708123
## 883 884 885 886 887 888
## 24.87057883 22.79513082 5.41737383 14.57085481 -19.67394377 20.47771204
## 889 890 891 892 893 894
## -19.67394377 2.38518885 31.21082225 14.14187474 40.56114531 19.41878700
## 895 896 897 898 899 900
## 12.52114770 15.77849070 17.21657170 14.57085481 5.41737383 4.01189543
## 901 902 903 904 905 906
## 22.79513082 24.87057883 42.19839377 22.84708123 21.38808413 -15.70302056
## 907 908 909 910 911 912
## 25.84952037 14.97792935 17.30681359 22.09150953 38.58809746 0.29560501
## 913 914 915 916 917 918
## 7.53228131 23.16628381 -20.25308362 21.95476771 -35.70579721 18.52113905
## 919 920 921 922 923 924
## 26.53600617 24.16394141 27.17795407 30.71950463 28.60096859 -26.90275792
## 925 926 927 928 929 930
## -25.14463337 -11.65141606 5.29804415 -21.15613262 28.03168242 29.18981536
## 931 932 933 934 935 936
## 24.92664789 23.95877256 29.41086343 -16.62384077 -14.17969207 11.90495286
## 937 938 939 940 941 942
## 14.07320695 9.33821059 14.05271453 1.10721436 40.41211926 9.97039875
## 943 944 945 946 947 948
## -31.65199201 20.87483307 8.99936190 11.04572063 -15.84349537 -11.32963035
## 949 950 951 952 953 954
## 8.76847841 -3.19220259 19.79750635 -23.96921891 7.19599641 24.77472655
## 955 956 957 958 959 960
## 27.17459104 3.16718509 1.60389171 10.88717834 35.36847681 -34.25737252
## 961 962 963 964 965 966
## 28.09996931 29.62011449 9.60528304 6.50293659 -11.03784817 34.93592084
## 967 968 969 970 971 972
## -24.89527706 0.76431899 -6.39621598 25.04351917 24.75264658 26.34800926
## 973 974 975 976 977 978
## 32.06075927 9.74188936 -32.10957717 12.44011790 -1.90547914 19.82117680
## 979 980 981 982 983 984
## 10.44432344 14.96383612 22.14776589 32.94276825 19.16324209 6.83009272
## 985 986 987 988 989 990
## 15.44866838 19.09887542 41.72162806 35.67596992 18.18914652 11.39640353
## 991 992 993 994 995 996
## -3.18070109 -2.73182628 12.51637227 31.21798487 14.21213378 6.13641332
## 997 998 999 1000 1001 1002
## -12.87872763 2.75693885 6.13810295 51.13664317 -26.64277128 -43.77405023
## 1003 1004 1005 1006 1007 1008
## -17.43378579 31.58339929 19.81782751 -2.98141729 -2.09636655 4.39172363
## 1009 1010 1011 1012 1013 1014
## 7.93483424 0.61075338 -25.57099998 43.65046407 19.46778643 -11.64459376
## 1015 1016 1017 1018 1019 1020
## -13.93251466 21.92244719 24.63334358 6.56770794 11.09927125 40.86638424
## 1021 1022 1023 1024 1025 1026
## 43.44212529 8.24950575 14.42154140 5.06423831 -30.94998715 -25.56185167
## 1027 1028 1029 1030 1031 1032
## 23.57338547 31.04119603 24.04713908 44.63686577 -2.21007367 17.60799897
## 1033 1034 1035 1036 1037 1038
## 5.11390521 -13.12747614 26.22854888 18.87355066 13.36736191 35.09240475
## 1039 1040 1041 1042 1043 1044
## -39.15598354 8.43704320 5.74738111 -34.31340763 -18.91798717 28.56217129
## 1045 1046 1047 1048 1049 1050
## 32.52004975 34.43169941 22.87499167 10.12897780 41.42006788 11.14952998
## 1051 1052 1053 1054 1055 1056
## -23.16264781 29.17707635 33.47660803 29.18656084 9.45700605 -3.45341969
## 1057 1058 1059 1060 1061 1062
## -14.66360980 -11.97534729 -27.83325527 1.99787819 10.18525532 4.46915546
## 1063 1064 1065 1066 1067 1068
## -48.95764851 5.37123732 -29.33804655 8.71024032 32.64905574 19.23709935
## 1069 1070 1071 1072 1073 1074
## -3.53608039 28.06262374 11.28980328 17.47562179 42.98279904 43.02795477
## 1075 1076 1077 1078 1079 1080
## -6.64756630 56.50033319 20.93381915 22.22109504 -22.38835624 -6.83759156
## 1081 1082 1083 1084 1085 1086
## -35.95553724 -17.92655235 -5.95828349 7.80366781 -3.27899884 10.29546947
## 1087 1088 1089 1090 1091 1092
## -9.65097341 6.36054514 14.26469733 43.27623766 -7.90243137 11.97497838
## 1093 1094 1095 1096 1097 1098
## -3.55964238 -6.31951896 -14.31649546 15.76253912 15.04632596 7.34739203
## 1099 1100 1101 1102 1103 1104
## 27.66312113 17.80191720 31.88053030 18.69573458 26.68846167 17.80398312
## 1105 1106 1107 1108 1109 1110
## -2.67278468 -18.84790623 46.47953243 10.18327716 17.43944897 17.89947561
## 1111 1112 1113 1114 1115 1116
## -47.44009302 27.91319729 26.64915006 -1.78058849 36.26438162 -30.29992303
## 1117 1118 1119 1120 1121 1122
## 4.92153975 22.27951051 -31.40694089 -13.89043973 -9.08082697 18.99367012
## 1123 1124 1125 1126 1127 1128
## -25.72948140 -36.32386135 -3.60721160 8.62347064 8.30696872 0.88259606
## 1129 1130 1131 1132 1133 1134
## -0.08039741 9.54633575 13.03897706 -42.91413252 -56.01059094 19.68473402
## 1135 1136 1137 1138 1139 1140
## -30.38117403 28.15849857 10.01366310 -9.19499623 -28.49878827 -25.80228000
## 1141 1142 1143 1144 1145 1146
## 3.72489479 27.64361061 15.40683425 6.91097706 -7.73336673 20.03591224
## 1147 1148 1149 1150 1151 1152
## 3.45293478 -8.40875435 4.90952510 30.33917290 20.62561235 -3.42081489
## 1153 1154 1155 1156 1157 1158
## -28.97816140 16.68633824 0.57333402 30.37258257 2.43650278 7.63885361
## 1159 1160 1161 1162 1163 1164
## 12.24293823 -29.79410577 -2.35385424 29.61810832 27.82756735 14.99826792
## 1165 1166 1167 1168 1169 1170
## -8.20256811 29.20823530 -10.31895287 1.17569230 32.58761958 -14.66033701
## 1171 1172 1173 1174 1175 1176
## 18.82302309 31.18890318 0.14532567 5.05661624 9.47784763 26.74343201
## 1177 1178 1179 1180 1181 1182
## 31.36325542 25.63485960 14.73801395 -1.55445666 16.53334603 -0.82046526
## 1183 1184 1185 1186 1187 1188
## 34.18164860 -39.67606363 -21.00806359 -17.74201977 18.17519840 -15.85152389
## 1189 1190
## 29.79909918 22.22593892
#Anova Table
anova(fit)
## Analysis of Variance Table
##
## Response: max.heart.rate
## Df Sum Sq Mean Sq F value Pr(>F)
## age 1 105233 105233 202.217 < 2.2e-16 ***
## sex 1 24062 24062 46.237 1.657e-11 ***
## cholesterol 1 27536 27536 52.914 6.320e-13 ***
## resting.bp.s 1 716 716 1.376 0.241
## Residuals 1185 616670 520
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
vcov(fit)
## (Intercept) age sex cholesterol
## (Intercept) 33.462047666 -2.005976e-01 -2.2865892775 -9.290449e-03
## age -0.200597615 5.383348e-03 -0.0002042404 3.593589e-05
## sex -2.286589278 -2.042404e-04 2.5351069578 2.227442e-03
## cholesterol -0.009290449 3.593589e-05 0.0022274423 4.517105e-05
## resting.bp.s -0.140348466 -7.264291e-04 -0.0008133942 -2.908624e-05
## resting.bp.s
## (Intercept) -1.403485e-01
## age -7.264291e-04
## sex -8.133942e-04
## cholesterol -2.908624e-05
## resting.bp.s 1.408302e-03
cov2cor(vcov(fit))
## (Intercept) age sex cholesterol resting.bp.s
## (Intercept) 1.0000000 -0.472632167 -0.248264008 -0.23896282 -0.64652241
## age -0.4726322 1.000000000 -0.001748306 0.07287392 -0.26382695
## sex -0.2482640 -0.001748306 1.000000000 0.20815087 -0.01361304
## cholesterol -0.2389628 0.072873917 0.208150865 1.00000000 -0.11532134
## resting.bp.s -0.6465224 -0.263826953 -0.013613040 -0.11532134 1.00000000
temp <- influence.measures(fit)
temp
## Influence measures of
## lm(formula = max.heart.rate ~ age + sex + cholesterol + resting.bp.s, data = heart) :
##
## dfb.1_ dfb.age dfb.sex dfb.chls dfb.rs.. dffit cov.r cook.d
## 1 4.79e-03 -3.55e-02 1.64e-02 1.69e-02 1.68e-02 0.048930 1.006 4.79e-04
## 2 -1.37e-03 -1.02e-02 -2.04e-02 -9.64e-03 1.88e-02 0.030167 1.011 1.82e-04
## 3 -5.72e-02 1.35e-01 -5.53e-02 -5.59e-02 -2.09e-02 -0.173481 0.980 5.99e-03
## 4 -3.58e-02 3.97e-02 1.02e-01 2.38e-02 -2.88e-02 -0.123610 0.993 3.05e-03
## 5 1.17e-02 4.43e-03 -9.30e-03 2.71e-03 -1.81e-02 -0.027255 1.005 1.49e-04
## 6 1.26e-02 -1.95e-02 1.23e-02 1.99e-02 -6.01e-03 0.034660 1.008 2.40e-04
## 7 1.90e-02 -1.67e-02 -3.25e-02 -3.08e-03 2.32e-03 0.041236 1.007 3.40e-04
## 8 3.56e-03 1.65e-03 2.66e-03 1.11e-03 -5.83e-03 0.007853 1.007 1.23e-05
## 9 -1.69e-02 5.86e-02 -1.66e-02 3.04e-03 -2.76e-02 -0.068896 1.004 9.49e-04
## 10 -5.17e-02 1.79e-02 7.60e-02 -1.81e-02 2.65e-02 -0.101903 0.998 2.07e-03
## 11 -3.90e-02 4.66e-02 4.69e-02 1.27e-02 -1.00e-02 -0.071003 1.007 1.01e-03
## 12 1.15e-02 -1.57e-02 -1.92e-02 1.41e-02 -5.73e-03 -0.052589 0.997 5.53e-04
## 13 -1.08e-02 1.31e-02 -5.10e-03 -1.27e-04 2.33e-03 -0.017694 1.007 6.27e-05
## 14 4.96e-04 2.49e-03 -2.44e-03 -1.07e-03 -2.18e-03 -0.005605 1.006 6.29e-06
## 15 -4.84e-02 2.78e-02 4.87e-02 9.59e-03 1.62e-02 -0.067005 1.006 8.98e-04
## 16 7.27e-04 2.25e-04 -1.45e-03 2.87e-04 -6.39e-04 0.001886 1.008 7.12e-07
## 17 2.72e-02 -2.35e-02 9.23e-03 -1.61e-04 -1.30e-02 0.036177 1.007 2.62e-04
## 18 1.79e-02 -1.13e-02 -2.06e-02 -5.42e-03 -3.80e-03 0.027105 1.009 1.47e-04
## 19 -9.45e-03 -1.55e-02 -8.67e-03 -9.83e-03 2.66e-02 -0.032313 1.009 2.09e-04
## 20 3.05e-03 -4.40e-03 1.77e-03 1.59e-03 -6.18e-04 0.005839 1.009 6.82e-06
## 21 -4.73e-02 1.44e-02 3.70e-02 2.71e-03 3.11e-02 -0.058032 1.009 6.74e-04
## 22 -5.43e-03 5.02e-03 -2.87e-03 8.13e-04 2.09e-03 -0.008803 1.006 1.55e-05
## 23 1.98e-02 -7.06e-03 -3.22e-02 -8.06e-03 -5.02e-03 0.038118 1.007 2.91e-04
## 24 5.56e-05 1.99e-04 -1.11e-04 -1.10e-04 -1.85e-04 -0.000330 1.008 2.18e-08
## 25 -1.28e-02 2.50e-02 -9.80e-03 -1.15e-03 -4.48e-03 -0.031764 1.006 2.02e-04
## 26 2.93e-02 -5.75e-02 1.70e-02 -7.34e-04 1.16e-02 0.067004 1.004 8.98e-04
## 27 -7.07e-03 -2.91e-03 -2.54e-02 -2.50e-02 1.89e-02 -0.052152 0.999 5.44e-04
## 28 -1.08e-02 -1.46e-03 -2.40e-02 -3.04e-02 2.39e-02 -0.052750 1.001 5.56e-04
## 29 -2.92e-02 -1.71e-02 5.46e-02 -1.00e-01 5.73e-02 -0.141108 1.004 3.98e-03
## 30 2.97e-03 -1.46e-03 3.62e-03 -5.77e-04 -2.11e-03 0.008423 1.005 1.42e-05
## 31 3.59e-02 1.35e-03 -3.59e-02 -9.37e-02 -1.13e-02 -0.102206 1.010 2.09e-03
## 32 -9.46e-04 -6.28e-03 -1.19e-02 7.22e-03 3.63e-03 -0.030323 1.002 1.84e-04
## 33 -3.95e-03 -3.10e-03 -1.27e-02 -6.44e-03 9.21e-03 -0.026328 1.003 1.39e-04
## 34 -1.88e-02 3.25e-02 -1.13e-02 8.32e-03 -6.63e-03 -0.042401 1.004 3.60e-04
## 35 -1.25e-04 3.43e-04 4.43e-04 1.94e-04 -3.21e-04 -0.000653 1.011 8.53e-08
## 36 -9.68e-03 1.73e-02 -5.12e-03 -3.30e-03 -1.30e-03 -0.020149 1.010 8.13e-05
## 37 6.46e-02 -6.83e-02 -4.33e-02 -6.41e-02 2.70e-04 -0.114004 0.992 2.59e-03
## 38 -4.75e-02 2.54e-02 4.22e-02 -1.51e-03 2.20e-02 -0.063524 1.007 8.07e-04
## 39 -4.09e-03 1.39e-03 5.56e-03 2.02e-03 1.34e-03 -0.006769 1.009 9.17e-06
## 40 -4.81e-03 2.43e-02 4.98e-02 1.03e-02 -3.25e-02 -0.067326 1.006 9.07e-04
## 41 2.96e-03 4.43e-03 3.67e-02 6.04e-03 -2.04e-02 -0.046590 1.007 4.34e-04
## 42 -2.76e-02 -8.19e-03 1.06e-01 -3.08e-02 1.30e-02 -0.135227 0.988 3.65e-03
## 43 2.28e-03 -3.09e-02 9.02e-03 5.30e-03 2.00e-02 0.037706 1.010 2.85e-04
## 44 -1.24e-02 -9.91e-03 2.41e-02 1.99e-02 1.56e-02 0.049910 0.999 4.98e-04
## 45 -3.64e-02 3.53e-02 -1.73e-02 8.48e-03 1.17e-02 -0.057578 1.001 6.63e-04
## 46 1.13e-02 -1.62e-02 -1.85e-02 -2.94e-02 9.52e-03 -0.042117 1.004 3.55e-04
## 47 2.11e-02 -2.78e-02 1.02e-02 3.19e-03 -3.72e-03 0.035897 1.007 2.58e-04
## 48 -4.87e-03 -1.93e-02 2.10e-02 3.44e-03 1.97e-02 0.048911 0.999 4.78e-04
## 49 3.74e-02 -4.42e-02 2.43e-02 4.01e-02 -2.21e-02 0.076306 1.006 1.16e-03
## 50 2.45e-02 -1.98e-02 1.46e-02 1.86e-02 -1.91e-02 0.042852 1.006 3.67e-04
## 51 -5.28e-03 1.00e-02 -1.70e-02 -9.12e-03 1.31e-03 -0.034542 1.002 2.39e-04
## 52 -9.66e-02 3.94e-02 1.29e-01 2.88e-02 3.23e-02 -0.158482 0.984 5.00e-03
## 53 -3.41e-03 3.35e-02 -1.85e-02 -4.21e-03 -2.11e-02 -0.051139 1.002 5.23e-04
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## 533 2.63e-02 -2.31e-02 -1.67e-02 -2.43e-02 -4.29e-03 -0.043017 1.005 3.70e-04
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## 536 -1.18e-04 1.19e-03 1.01e-03 5.52e-04 -9.86e-04 0.002411 1.006 1.16e-06
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## 539 -2.36e-02 2.56e-02 8.27e-03 8.25e-03 4.51e-03 0.032576 1.009 2.12e-04
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## 543 6.66e-04 2.53e-02 3.41e-03 -4.55e-03 -1.92e-02 0.031232 1.014 1.95e-04
## 544 -1.04e-02 3.41e-04 9.51e-02 -1.27e-02 -1.53e-02 -0.116496 0.992 2.71e-03
## 545 -2.64e-02 1.45e-02 5.89e-03 -2.18e-03 2.00e-02 0.031689 1.010 2.01e-04
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## 548 5.93e-03 -1.46e-02 1.37e-02 3.97e-03 3.25e-03 0.030724 1.003 1.89e-04
## 549 2.84e-02 -2.48e-02 -2.05e-02 -2.83e-04 -1.33e-02 -0.054250 0.999 5.88e-04
## 550 -7.28e-04 2.28e-02 9.23e-03 1.16e-02 -2.10e-02 0.032690 1.008 2.14e-04
## 551 -1.53e-02 2.33e-02 7.97e-03 -1.75e-03 -4.49e-05 0.030452 1.006 1.86e-04
## 552 1.38e-01 3.45e-02 -5.29e-02 -3.07e-02 -1.78e-01 -0.207965 0.976 8.60e-03
## 553 2.21e-03 -6.34e-02 -3.42e-02 -2.08e-02 5.45e-02 -0.100054 0.990 2.00e-03
## 554 2.37e-02 -2.98e-02 -9.85e-03 -4.92e-03 -2.49e-03 -0.037343 1.007 2.79e-04
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## 556 -2.29e-02 -1.39e-02 1.47e-02 -1.23e-02 4.18e-02 0.055313 1.002 6.12e-04
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## 558 2.85e-02 -2.38e-02 -8.91e-03 -1.33e-02 -9.85e-03 -0.034761 1.011 2.42e-04
## 559 5.39e-03 -3.01e-03 -9.47e-03 -1.37e-03 -3.44e-03 -0.020144 1.004 8.12e-05
## 560 6.49e-03 -5.62e-03 -8.21e-03 -4.59e-03 -1.57e-03 -0.017311 1.005 6.00e-05
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## 562 9.67e-06 -2.11e-06 -9.76e-05 -7.11e-06 -7.20e-06 -0.000203 1.005 8.22e-09
## 563 2.04e-04 7.01e-05 3.14e-03 -1.03e-03 5.30e-05 0.007141 1.005 1.02e-05
## 564 -1.75e-02 1.21e-02 1.63e-02 1.77e-02 4.89e-03 0.035398 1.003 2.51e-04
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## 566 -2.27e-02 6.69e-03 2.00e-02 1.96e-02 1.45e-02 0.043381 1.002 3.76e-04
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## 568 -1.98e-03 4.18e-02 -1.16e-02 1.23e-02 -3.49e-02 -0.056509 1.006 6.39e-04
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## 570 -9.56e-02 9.13e-02 -5.08e-02 -6.30e-02 6.04e-02 -0.160335 0.986 5.12e-03
## 571 3.48e-02 7.92e-03 -1.85e-02 -8.87e-04 -4.64e-02 -0.060232 1.002 7.25e-04
## 572 5.48e-04 -7.18e-03 -1.33e-02 -6.49e-03 7.21e-03 -0.027503 1.003 1.51e-04
## 573 9.95e-03 -1.71e-02 -3.96e-03 9.46e-03 -1.23e-03 -0.024561 1.008 1.21e-04
## 574 -1.30e-02 9.45e-03 5.67e-03 -1.01e-03 7.96e-03 0.019109 1.006 7.31e-05
## 575 -3.48e-02 2.99e-02 6.94e-03 -1.56e-02 2.21e-02 0.050689 1.008 5.14e-04
## 576 1.64e-02 -2.13e-02 -7.67e-03 -2.39e-03 -1.43e-03 -0.027523 1.007 1.52e-04
## 577 8.22e-03 -3.84e-03 -1.18e-02 -1.37e-02 -1.92e-03 -0.023938 1.005 1.15e-04
## 578 5.96e-03 -7.62e-03 -4.62e-03 2.62e-03 -1.80e-03 -0.014305 1.006 4.10e-05
## 579 4.63e-02 -3.96e-02 -2.55e-02 -5.00e-02 -5.82e-03 -0.073074 1.006 1.07e-03
## 580 1.60e-02 3.55e-04 -7.66e-03 6.37e-03 -2.11e-02 -0.028940 1.006 1.68e-04
## 581 3.15e-02 -3.30e-02 -1.53e-02 -2.02e-02 -3.85e-03 -0.047070 1.006 4.43e-04
## 582 -2.88e-03 3.16e-03 -4.29e-03 4.71e-03 -7.20e-04 -0.012312 1.005 3.03e-05
## 583 -1.86e-04 -1.56e-02 1.15e-02 -6.77e-05 1.25e-02 0.029657 1.004 1.76e-04
## 584 2.40e-02 -9.45e-02 -2.99e-02 -1.87e-02 5.30e-02 -0.115198 0.995 2.65e-03
## 585 -3.08e-04 3.67e-04 1.58e-04 1.83e-04 7.54e-06 0.000494 1.008 4.89e-08
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## 587 4.45e-02 6.21e-03 -1.43e-02 -1.23e-02 -5.25e-02 -0.061000 1.009 7.44e-04
## 588 -5.42e-03 -1.54e-03 -1.51e-02 -1.17e-02 1.15e-02 -0.031099 1.003 1.93e-04
## 589 1.52e-02 -1.90e-02 7.55e-03 4.41e-03 -4.17e-03 0.025580 1.008 1.31e-04
## 590 4.26e-03 -5.62e-03 -2.39e-03 -1.08e-03 -1.60e-04 -0.007581 1.007 1.15e-05
## 591 4.69e-02 -7.00e-02 -2.00e-02 -1.63e-02 6.09e-03 -0.081279 1.004 1.32e-03
## 592 -4.47e-03 7.69e-03 3.84e-03 -2.40e-03 -6.52e-05 0.012615 1.006 3.19e-05
## 593 -2.98e-02 -3.09e-02 -1.93e-02 -1.26e-02 6.33e-02 -0.074867 1.004 1.12e-03
## 594 -6.23e-02 -5.94e-05 1.57e-02 1.33e-02 6.82e-02 0.078120 1.011 1.22e-03
## 595 3.58e-04 -7.18e-04 -3.98e-04 -4.16e-04 2.89e-04 -0.001056 1.007 2.23e-07
## 596 3.84e-02 -2.52e-03 -1.78e-02 -1.21e-02 -3.87e-02 -0.054169 1.004 5.87e-04
## 597 -2.57e-03 8.39e-03 6.11e-03 -7.61e-04 -3.37e-03 0.016023 1.005 5.14e-05
## 598 -2.09e-03 -2.67e-02 -3.32e-02 -3.64e-02 3.58e-02 -0.075117 0.995 1.13e-03
## 599 -5.67e-05 9.81e-05 4.60e-04 -1.21e-04 2.91e-05 0.001038 1.005 2.16e-07
## 600 -4.35e-03 -4.64e-03 -8.47e-03 -5.09e-03 1.04e-02 -0.019474 1.005 7.59e-05
## 601 2.35e-03 -1.33e-02 -2.64e-02 -3.62e-03 8.95e-03 -0.056347 0.994 6.34e-04
## 602 5.49e-03 -1.93e-02 -2.77e-02 -6.13e-03 1.09e-02 -0.059924 0.993 7.17e-04
## 603 1.24e-02 -1.06e-02 -1.02e-02 -1.24e-02 -1.96e-03 -0.023475 1.006 1.10e-04
## 604 1.37e-02 -5.49e-02 -4.28e-02 -7.82e-02 5.37e-02 -0.114120 0.996 2.60e-03
## 605 1.81e-02 -4.17e-03 -1.12e-02 -2.42e-03 -1.70e-02 -0.029792 1.004 1.78e-04
## 606 2.89e-02 -2.64e-02 -1.01e-02 -1.53e-02 -7.70e-03 -0.037184 1.010 2.77e-04
## 607 -2.99e-02 5.01e-02 2.07e-02 2.10e-02 -1.17e-02 0.064179 1.003 8.24e-04
## 608 -9.01e-02 -6.05e-04 1.23e-01 -1.41e-02 6.99e-02 -0.163656 0.983 5.33e-03
## 609 4.63e-02 -1.55e-02 -1.86e-02 -1.30e-02 -3.73e-02 -0.058799 1.003 6.91e-04
## 610 1.18e-02 3.52e-03 -1.37e-02 -1.74e-02 -1.06e-02 -0.030104 1.005 1.81e-04
## 611 -1.87e-02 7.16e-03 6.60e-03 -5.63e-03 1.81e-02 0.027630 1.006 1.53e-04
## 612 -2.09e-03 2.48e-02 -2.38e-02 -3.23e-02 -6.31e-03 -0.054980 1.002 6.04e-04
## 613 1.15e-03 5.19e-04 -4.04e-03 2.31e-03 -1.08e-03 0.005820 1.009 6.78e-06
## 614 -5.36e-03 1.12e-02 5.65e-03 -7.63e-03 -6.76e-05 0.021147 1.005 8.95e-05
## 615 -1.19e-02 -1.45e-02 -2.89e-02 -1.55e-02 3.05e-02 -0.064240 0.994 8.24e-04
## 616 8.63e-03 -4.35e-03 -8.34e-03 -1.68e-02 -9.64e-04 -0.020315 1.008 8.26e-05
## 617 6.12e-03 -5.72e-02 -3.38e-02 -3.58e-02 5.01e-02 -0.093410 0.994 1.74e-03
## 618 2.59e-02 -4.64e-02 -1.94e-02 -3.38e-02 1.78e-02 -0.062106 1.007 7.72e-04
## 619 -3.87e-03 2.18e-02 -1.18e-02 3.74e-02 -1.91e-02 0.048703 1.021 4.75e-04
## 620 -9.95e-05 2.30e-03 2.99e-03 3.13e-03 -2.75e-03 0.006568 1.006 8.63e-06
## 621 1.78e-02 -4.08e-02 -2.24e-02 -2.51e-02 1.99e-02 -0.060223 1.002 7.25e-04
## 622 2.20e-03 -2.89e-02 1.99e-02 -5.32e-03 1.54e-02 -0.038452 1.013 2.96e-04
## 623 -1.64e-03 2.52e-02 9.05e-03 -8.96e-04 -1.77e-02 0.034671 1.006 2.41e-04
## 624 -9.09e-04 1.62e-03 3.40e-03 3.14e-03 -1.28e-03 0.006799 1.006 9.25e-06
## 625 3.83e-03 8.16e-03 5.62e-03 5.20e-03 -1.26e-02 0.017227 1.007 5.94e-05
## 626 -3.71e-02 2.81e-02 3.23e-02 4.20e-02 6.88e-03 0.072608 0.997 1.05e-03
## 627 -1.06e-02 9.25e-03 -1.46e-02 1.60e-02 5.44e-03 0.029193 1.011 1.71e-04
## 628 -1.61e-02 1.94e-02 2.13e-02 1.32e-02 -9.85e-04 0.045959 1.000 4.22e-04
## 629 1.38e-02 7.68e-03 -2.10e-02 -7.33e-03 -1.96e-02 -0.046156 0.999 4.26e-04
## 630 5.52e-03 -4.82e-02 2.52e-02 9.76e-03 2.83e-02 0.070656 0.998 9.98e-04
## 631 -8.86e-03 1.32e-02 1.02e-02 6.73e-03 -2.39e-03 0.023907 1.005 1.14e-04
## 632 4.74e-03 7.24e-03 -2.38e-02 8.90e-03 -6.04e-03 0.032090 1.007 2.06e-04
## 633 -1.67e-03 -6.57e-03 5.91e-03 2.22e-03 4.69e-03 -0.010012 1.014 2.01e-05
## 634 5.86e-03 3.42e-02 -2.95e-02 -3.90e-02 -2.07e-02 -0.071130 1.000 1.01e-03
## 635 -5.67e-03 -4.46e-03 1.20e-02 -2.99e-04 1.02e-02 0.027148 1.003 1.47e-04
## 636 4.69e-03 2.81e-02 1.12e-02 6.74e-03 -2.99e-02 0.042655 1.007 3.64e-04
## 637 1.55e-02 -5.90e-02 1.93e-02 -5.70e-03 3.05e-02 0.073417 1.001 1.08e-03
## 638 -9.81e-04 5.07e-03 1.87e-03 1.50e-03 -3.37e-03 0.006570 1.008 8.64e-06
## 639 1.19e-02 -2.57e-02 2.87e-02 1.95e-02 -1.39e-04 0.061129 0.996 7.46e-04
## 640 3.31e-02 -3.05e-02 2.75e-02 3.83e-02 -2.74e-02 0.072688 1.002 1.06e-03
## 641 -2.45e-03 1.02e-03 -1.30e-03 -2.97e-04 2.15e-03 -0.003749 1.007 2.81e-06
## 642 4.50e-03 1.13e-03 -2.02e-02 4.94e-03 -9.99e-04 0.025313 1.007 1.28e-04
## 643 -1.59e-02 1.10e-02 3.40e-02 -4.85e-03 1.10e-04 -0.043121 1.006 3.72e-04
## 644 -2.33e-03 3.13e-03 6.05e-03 5.18e-04 -1.86e-03 -0.007758 1.009 1.20e-05
## 645 4.53e-03 -2.56e-04 -7.84e-03 2.54e-03 -3.25e-03 0.010607 1.008 2.25e-05
## 646 1.65e-02 2.96e-02 2.34e-02 1.82e-02 -4.87e-02 0.068242 1.000 9.31e-04
## 647 -1.41e-03 -9.35e-03 6.97e-03 -1.86e-03 7.35e-03 -0.013562 1.014 3.68e-05
## 648 -1.66e-03 7.94e-03 1.10e-02 6.54e-03 -6.53e-03 0.023298 1.004 1.09e-04
## 649 -2.71e-02 1.50e-02 9.09e-03 3.35e-03 1.86e-02 0.033334 1.007 2.22e-04
## 650 1.77e-02 -1.57e-02 -1.71e-02 -3.68e-03 -1.70e-03 0.025790 1.010 1.33e-04
## 651 -7.98e-03 4.20e-04 3.17e-03 4.40e-03 7.48e-03 0.010518 1.010 2.21e-05
## 652 4.39e-03 1.09e-02 -9.81e-03 1.72e-03 -1.43e-02 -0.026348 1.004 1.39e-04
## 653 1.35e-03 -3.18e-03 3.73e-03 3.07e-03 -8.95e-05 0.007899 1.006 1.25e-05
## 654 -6.69e-03 6.67e-03 5.38e-03 8.91e-04 2.22e-03 0.013636 1.005 3.72e-05
## 655 1.82e-02 -2.64e-03 -8.35e-03 -7.57e-03 -1.65e-02 -0.024688 1.007 1.22e-04
## 656 2.30e-03 -4.01e-03 1.58e-03 -8.41e-04 7.72e-04 0.005394 1.007 5.82e-06
## 657 3.28e-02 -2.53e-02 3.20e-02 1.37e-02 -2.29e-02 0.073694 0.992 1.08e-03
## 658 -2.57e-03 -7.03e-02 2.26e-02 2.31e-04 5.84e-02 0.093309 1.002 1.74e-03
## 659 1.38e-02 3.28e-02 -5.78e-02 -8.69e-03 -2.13e-02 0.074800 1.004 1.12e-03
## 660 1.98e-02 -4.03e-02 2.43e-02 1.11e-02 5.01e-03 0.062041 0.999 7.69e-04
## 661 2.01e-02 -5.18e-03 7.31e-03 1.60e-03 -1.98e-02 0.026967 1.007 1.46e-04
## 662 -7.04e-05 4.98e-04 4.29e-04 2.03e-04 -3.80e-04 0.001015 1.006 2.06e-07
## 663 -2.17e-02 1.43e-02 2.26e-02 4.34e-03 1.25e-02 0.051314 0.997 5.26e-04
## 664 -1.57e-02 6.33e-03 -7.97e-03 7.97e-03 1.06e-02 -0.026268 1.005 1.38e-04
## 665 5.01e-02 -2.86e-02 2.11e-02 1.85e-03 -3.64e-02 0.069016 1.000 9.52e-04
## 666 1.51e-02 -8.23e-03 -5.26e-03 -3.37e-03 -9.93e-03 -0.018320 1.008 6.72e-05
## 667 1.92e-02 -2.70e-02 4.93e-02 7.02e-03 -1.87e-02 -0.067644 1.006 9.15e-04
## 668 -7.12e-03 4.74e-02 -2.92e-02 -3.93e-02 -1.59e-02 -0.077000 1.001 1.19e-03
## 669 1.30e-02 -7.60e-03 3.19e-02 4.38e-03 -1.06e-02 0.066891 0.989 8.93e-04
## 670 -1.23e-02 1.97e-02 -2.15e-02 2.68e-02 -1.56e-03 0.045337 1.011 4.11e-04
## 671 -9.13e-03 4.97e-02 -1.03e-01 -2.83e-02 1.19e-02 0.129590 0.994 3.35e-03
## 672 2.61e-02 -2.27e-02 -4.44e-02 -4.94e-03 3.24e-03 0.056132 1.005 6.30e-04
## 673 2.70e-02 -1.21e-02 -2.20e-02 -5.18e-03 -1.35e-02 0.032931 1.010 2.17e-04
## 674 2.24e-03 -2.99e-03 -2.04e-03 1.36e-03 -7.09e-04 -0.006179 1.006 7.64e-06
## 675 -4.20e-02 -4.71e-02 1.04e-01 3.19e-02 4.45e-02 -0.132596 0.994 3.51e-03
## 676 -3.42e-03 -2.27e-05 -4.58e-03 -5.66e-04 5.63e-03 0.007853 1.012 1.23e-05
## 677 7.37e-03 -4.55e-02 -2.86e-02 -3.88e-02 4.04e-02 -0.077768 1.000 1.21e-03
## 678 -3.58e-02 1.83e-03 2.07e-02 -4.58e-02 5.56e-02 0.094914 0.991 1.80e-03
## 679 -8.13e-03 2.84e-03 2.36e-02 -8.25e-03 1.86e-03 -0.031105 1.007 1.94e-04
## 680 2.34e-02 -2.33e-02 1.61e-02 7.31e-03 -1.13e-02 0.042722 1.003 3.65e-04
## 681 -1.88e-02 1.76e-02 -6.94e-02 -5.72e-03 3.17e-02 0.090002 1.001 1.62e-03
## 682 -2.71e-02 2.22e-02 1.58e-02 8.85e-03 1.10e-02 0.042118 1.003 3.55e-04
## 683 3.24e-02 -4.62e-03 -2.22e-02 -2.23e-02 -2.67e-02 -0.053143 1.001 5.65e-04
## 684 -1.63e-02 -2.12e-02 3.71e-02 3.10e-02 2.53e-02 0.078060 0.991 1.22e-03
## 685 -3.66e-04 3.14e-03 -1.01e-02 4.58e-03 -5.83e-05 0.014017 1.008 3.93e-05
## 686 -1.63e-02 9.01e-03 1.89e-02 5.07e-04 5.70e-03 -0.025288 1.008 1.28e-04
## 687 7.38e-03 -2.35e-03 4.28e-03 3.61e-03 -7.95e-03 0.012186 1.007 2.97e-05
## 688 -6.50e-04 8.02e-03 5.33e-03 5.95e-03 -7.57e-03 0.014130 1.007 4.00e-05
## 689 7.93e-03 1.05e-02 -2.44e-02 1.89e-02 -1.49e-02 0.040503 1.008 3.28e-04
## 690 -4.70e-02 3.77e-02 1.59e-02 1.14e-02 2.12e-02 0.058831 1.005 6.92e-04
## 691 8.45e-03 -2.33e-02 1.86e-02 3.86e-03 1.65e-03 -0.031702 1.012 2.01e-04
## 692 7.11e-03 1.66e-02 -1.59e-02 2.14e-04 -1.65e-02 0.027760 1.012 1.54e-04
## 693 7.73e-04 4.73e-03 -3.50e-03 -4.47e-03 -3.13e-03 -0.008868 1.007 1.57e-05
## 694 1.43e-03 -5.35e-04 5.72e-04 2.03e-04 -1.31e-03 0.001951 1.008 7.62e-07
## 695 6.35e-02 -2.45e-02 -4.20e-02 -8.43e-03 -3.89e-02 0.071877 1.010 1.03e-03
## 696 3.22e-02 -2.20e-02 -3.60e-02 -8.10e-03 -6.30e-03 0.048368 1.007 4.68e-04
## 697 1.23e-02 2.34e-02 3.26e-02 2.46e-02 -4.10e-02 0.075708 0.993 1.14e-03
## 698 2.82e-02 -9.88e-03 -2.08e-02 -5.08e-03 -2.34e-02 -0.050950 0.999 5.19e-04
## 699 -4.67e-02 6.22e-02 -1.81e-02 2.58e-03 4.40e-03 -0.075665 1.003 1.14e-03
## 700 3.33e-02 -7.95e-03 -2.16e-02 -2.04e-02 -2.57e-02 -0.052252 1.001 5.46e-04
## 701 1.61e-02 -3.12e-02 1.32e-02 1.51e-03 5.40e-03 0.040869 1.004 3.34e-04
## 702 -7.46e-03 -8.05e-03 -6.62e-03 -2.28e-03 1.58e-02 -0.021116 1.006 8.92e-05
## 703 -2.70e-03 -5.42e-02 2.25e-02 9.37e-03 4.28e-02 0.075871 1.002 1.15e-03
## 704 -3.86e-03 1.25e-02 7.20e-03 2.40e-03 -6.16e-03 0.019452 1.005 7.57e-05
## 705 -3.08e-02 -8.29e-04 9.50e-03 6.74e-03 3.42e-02 0.040289 1.010 3.25e-04
## 706 -1.26e-04 1.28e-04 1.67e-04 -5.41e-05 6.56e-06 -0.000257 1.010 1.33e-08
## 707 1.02e-02 1.19e-02 -1.13e-02 -5.47e-03 -1.94e-02 -0.030302 1.005 1.84e-04
## 708 -2.44e-02 1.88e-02 2.31e-02 8.61e-03 1.07e-02 0.052343 0.998 5.48e-04
## 709 -6.84e-04 2.85e-02 -4.85e-02 2.77e-02 -1.38e-02 0.073851 1.004 1.09e-03
## 710 -4.94e-03 -7.79e-03 -2.79e-02 -2.98e-02 2.19e-02 -0.057985 0.998 6.72e-04
## 711 -3.02e-02 -1.38e-02 -2.23e-02 -8.54e-03 4.90e-02 -0.066014 0.999 8.71e-04
## 712 1.15e-02 -2.99e-03 2.07e-02 6.02e-03 -1.31e-02 0.043824 0.999 3.84e-04
## 713 -3.80e-02 1.42e-02 -2.80e-02 -3.35e-02 4.43e-02 -0.074438 1.000 1.11e-03
## 714 -1.13e-02 4.08e-02 1.95e-02 3.11e-02 -2.95e-02 0.059772 1.006 7.15e-04
## 715 2.19e-02 2.44e-02 1.61e-02 1.52e-02 -4.99e-02 0.059441 1.006 7.07e-04
## 716 5.10e-03 -1.11e-02 1.64e-02 -6.98e-03 -4.95e-04 -0.024711 1.009 1.22e-04
## 717 1.48e-02 -2.66e-03 -2.31e-02 1.11e-04 -7.82e-03 0.028558 1.007 1.63e-04
## 718 6.05e-02 -2.17e-02 -5.57e-02 -2.86e-02 -2.78e-02 0.077529 1.007 1.20e-03
## 719 2.45e-02 -1.20e-01 -4.52e-02 -4.12e-02 8.00e-02 -0.156118 0.983 4.85e-03
## 720 9.19e-03 -5.41e-03 -2.08e-02 2.30e-03 -3.38e-04 0.025819 1.007 1.33e-04
## 721 2.67e-02 1.18e-03 -1.19e-02 -1.22e-02 -2.79e-02 -0.037709 1.007 2.85e-04
## 722 -1.09e-02 2.20e-02 1.33e-02 1.31e-02 -9.10e-03 0.033894 1.005 2.30e-04
## 723 1.02e-02 -1.14e-02 1.74e-02 1.89e-02 -9.25e-03 0.037737 1.003 2.85e-04
## 724 9.87e-04 1.46e-04 4.82e-04 3.31e-04 -1.38e-03 0.001665 1.008 5.55e-07
## 725 -1.04e-02 9.23e-03 -3.46e-02 6.96e-04 1.57e-02 0.045715 1.007 4.18e-04
## 726 -2.03e-02 1.76e-02 1.95e-02 -9.12e-03 1.28e-02 0.052719 0.998 5.55e-04
## 727 -3.54e-02 1.31e-02 3.61e-02 1.56e-02 1.51e-02 -0.048017 1.008 4.61e-04
## 728 6.19e-02 1.95e-02 6.57e-02 -2.02e-02 -1.03e-01 -0.136644 1.006 3.73e-03
## 729 1.57e-03 -1.20e-03 7.20e-04 4.62e-04 -1.04e-03 0.002285 1.008 1.04e-06
## 730 -2.09e-02 8.55e-03 -3.71e-02 1.03e-02 2.67e-02 0.057002 1.007 6.50e-04
## 731 5.67e-03 1.54e-03 -4.15e-02 1.40e-02 1.73e-03 0.053930 1.005 5.82e-04
## 732 8.77e-03 -1.12e-02 8.04e-03 1.02e-02 -4.80e-03 0.021035 1.007 8.86e-05
## 733 6.64e-03 -5.53e-03 -1.88e-02 2.01e-03 2.17e-03 0.023442 1.007 1.10e-04
## 734 -3.35e-03 2.97e-03 -3.04e-03 -2.42e-03 2.37e-03 -0.007251 1.006 1.05e-05
## 735 3.34e-02 1.05e-02 2.60e-02 2.91e-04 -5.59e-02 -0.064265 1.019 8.27e-04
## 736 1.98e-02 -2.87e-02 4.72e-02 6.25e-03 -1.71e-02 -0.065939 1.006 8.70e-04
## 737 1.13e-02 -1.56e-02 -3.35e-02 -4.11e-02 1.30e-02 -0.068441 0.995 9.36e-04
## 738 -2.51e-03 1.25e-03 -1.85e-03 2.35e-04 1.85e-03 -0.004757 1.006 4.53e-06
## 739 -4.83e-03 -7.80e-03 -2.41e-02 -3.13e-02 2.23e-02 -0.052360 1.001 5.48e-04
## 740 6.76e-02 -7.05e-03 -4.29e-02 -4.13e-02 -5.92e-02 -0.106869 0.987 2.28e-03
## 741 -1.73e-02 1.17e-02 -1.90e-02 1.29e-02 1.35e-02 0.035532 1.011 2.53e-04
## 742 9.68e-04 2.58e-03 9.93e-03 1.13e-02 -6.96e-03 0.020468 1.005 8.38e-05
## 743 -1.07e-02 -9.46e-03 -4.57e-02 -1.60e-02 3.90e-02 0.064461 1.007 8.31e-04
## 744 6.67e-03 -4.99e-02 -3.04e-02 -3.67e-02 4.40e-02 -0.083149 0.998 1.38e-03
## 745 1.58e-02 -7.27e-03 -5.32e-02 -1.61e-02 8.82e-03 0.061241 1.004 7.50e-04
## 746 4.47e-04 -5.50e-03 1.33e-02 -6.84e-05 3.85e-03 0.028451 1.002 1.62e-04
## 747 5.14e-03 3.17e-02 2.10e-02 1.58e-02 -3.63e-02 0.058790 1.001 6.91e-04
## 748 2.96e-02 5.14e-02 -6.07e-02 1.59e-02 -6.02e-02 0.102177 1.005 2.09e-03
## 749 4.06e-04 1.05e-02 3.67e-03 2.30e-03 -9.50e-03 0.014507 1.009 4.21e-05
## 750 9.55e-03 -5.13e-02 2.18e-02 4.78e-03 2.78e-02 0.068506 1.001 9.38e-04
## 751 9.04e-03 -5.90e-02 -2.85e-02 -2.82e-02 4.55e-02 -0.085970 0.998 1.48e-03
## 752 -2.59e-02 -7.65e-03 2.08e-02 7.74e-03 3.36e-02 0.053249 1.000 5.67e-04
## 753 7.79e-03 -1.15e-02 -2.15e-02 -9.50e-03 9.50e-03 0.027798 1.009 1.55e-04
## 754 -4.71e-02 5.70e-02 -7.96e-02 1.26e-02 3.17e-02 0.122030 0.999 2.97e-03
## 755 1.74e-04 3.03e-03 5.12e-03 4.50e-03 -4.11e-03 0.010794 1.006 2.33e-05
## 756 7.25e-02 -6.73e-02 -6.23e-02 -1.55e-02 -6.84e-03 0.101436 1.006 2.06e-03
## 757 -7.88e-03 1.55e-02 2.39e-02 4.76e-03 -4.62e-03 0.051278 0.996 5.25e-04
## 758 -5.92e-03 5.40e-03 3.19e-03 7.63e-04 2.38e-03 0.009362 1.006 1.75e-05
## 759 -3.94e-02 3.21e-02 4.10e-02 4.38e-02 5.83e-03 0.087860 0.989 1.54e-03
## 760 -4.64e-03 -1.37e-02 1.62e-02 7.09e-03 1.38e-02 0.036160 1.002 2.62e-04
## 761 -7.50e-03 3.90e-03 -1.17e-02 -3.43e-03 6.80e-03 -0.024928 1.003 1.24e-04
## 762 -1.76e-01 -5.91e-02 4.92e-02 3.40e-02 2.40e-01 0.261219 0.989 1.36e-02
## 763 -1.05e-02 -6.61e-03 -4.40e-02 -5.45e-02 3.57e-02 -0.093062 0.988 1.73e-03
## 764 1.80e-02 2.96e-03 1.49e-02 1.04e-02 -2.68e-02 0.039156 1.004 3.07e-04
## 765 -7.34e-02 5.58e-02 -2.26e-02 1.31e-02 3.70e-02 -0.094417 0.997 1.78e-03
## 766 -1.37e-02 2.39e-02 2.93e-02 1.44e-02 -7.75e-03 0.062393 0.993 7.77e-04
## 767 2.39e-02 -1.38e-02 -2.21e-02 3.02e-03 -1.06e-02 0.033656 1.009 2.27e-04
## 768 4.29e-02 -3.62e-02 2.24e-02 1.84e-02 -2.76e-02 0.067505 1.002 9.11e-04
## 769 1.14e-02 -2.12e-03 -1.74e-02 -2.36e-03 -5.44e-03 0.021026 1.008 8.85e-05
## 770 2.91e-02 9.75e-03 -3.79e-02 7.87e-03 -3.16e-02 0.055872 1.007 6.25e-04
## 771 2.75e-03 -3.00e-02 3.96e-02 -1.58e-02 1.22e-02 -0.059558 1.007 7.10e-04
## 772 -1.66e-03 5.65e-04 4.23e-03 -1.78e-04 1.73e-04 -0.005045 1.008 5.10e-06
## 773 4.52e-02 -1.03e-02 -4.16e-02 -7.56e-03 -2.92e-02 0.059107 1.007 6.99e-04
## 774 1.29e-02 -9.26e-04 -1.88e-02 -4.71e-03 -1.28e-02 -0.040066 1.000 3.21e-04
## 775 8.31e-03 -2.01e-02 1.88e-02 2.57e-02 -2.47e-03 0.043907 1.004 3.86e-04
## 776 1.16e-02 1.43e-02 1.84e-02 1.35e-03 -2.53e-02 0.047076 1.000 4.43e-04
## 777 -7.36e-02 2.83e-02 -7.53e-02 -1.65e-02 9.19e-02 0.136295 1.005 3.71e-03
## 778 4.21e-02 -5.46e-02 2.20e-02 9.90e-03 -9.23e-03 0.073123 1.002 1.07e-03
## 779 -1.15e-02 1.31e-02 -3.43e-02 -1.74e-03 1.45e-02 0.045608 1.007 4.16e-04
## 780 -2.81e-03 4.24e-03 1.36e-02 1.34e-02 -4.57e-03 0.026866 1.004 1.44e-04
## 781 1.74e-03 -4.60e-03 -5.42e-03 -5.42e-03 3.42e-03 -0.011621 1.006 2.70e-05
## 782 2.05e-02 -1.31e-02 8.99e-03 2.79e-03 -1.45e-02 0.028763 1.006 1.66e-04
## 783 -3.66e-02 9.38e-03 -2.99e-02 1.01e-02 4.22e-02 0.062040 1.012 7.70e-04
## 784 1.20e-02 -3.70e-04 -1.40e-02 1.43e-03 -9.53e-03 0.019473 1.009 7.59e-05
## 785 2.19e-03 -1.05e-03 9.70e-03 -1.65e-04 -1.67e-03 0.020607 1.004 8.50e-05
## 786 -3.14e-03 4.32e-03 7.48e-03 9.67e-04 -2.44e-03 -0.009741 1.009 1.90e-05
## 787 -5.61e-02 6.77e-02 3.97e-02 5.01e-02 -5.02e-03 0.104978 0.992 2.20e-03
## 788 -1.90e-02 1.29e-02 5.92e-03 2.99e-03 1.09e-02 0.023009 1.008 1.06e-04
## 789 -3.26e-02 4.30e-02 1.74e-02 1.69e-02 -1.63e-03 0.055699 1.004 6.21e-04
## 790 -1.84e-03 -1.54e-02 -5.94e-03 -1.02e-02 1.77e-02 -0.023970 1.012 1.15e-04
## 791 -6.11e-03 -4.06e-02 4.20e-02 4.16e-03 2.48e-02 -0.064521 1.008 8.33e-04
## 792 3.71e-02 -4.64e-02 1.22e-02 -5.50e-03 -4.66e-03 0.056407 1.007 6.37e-04
## 793 1.29e-02 -4.12e-02 7.66e-02 -2.28e-02 -7.54e-04 -0.105913 0.998 2.24e-03
## 794 1.10e-02 1.01e-02 -2.13e-02 -2.67e-02 -1.18e-02 -0.045534 1.002 4.15e-04
## 795 -6.68e-04 -2.27e-03 1.23e-03 3.04e-04 2.47e-03 0.003847 1.007 2.96e-06
## 796 -2.56e-02 7.28e-02 3.00e-02 3.23e-02 -3.85e-02 0.094860 0.998 1.80e-03
## 797 9.01e-03 -1.07e-02 1.53e-02 -1.05e-03 -1.72e-03 0.034392 1.001 2.37e-04
## 798 5.28e-02 -6.02e-02 3.53e-02 2.22e-02 -2.14e-02 0.097914 0.992 1.91e-03
## 799 4.46e-04 -1.70e-03 6.42e-03 -7.42e-03 7.67e-04 -0.011959 1.010 2.86e-05
## 800 1.77e-02 -1.27e-02 5.82e-03 -2.63e-03 -9.72e-03 0.022965 1.007 1.06e-04
## 801 -1.08e-01 4.04e-02 8.51e-02 -1.38e-02 7.05e-02 -0.139365 0.998 3.88e-03
## 802 1.42e-04 -9.25e-04 2.68e-02 2.03e-02 -6.26e-03 0.051983 0.997 5.40e-04
## 803 4.00e-03 -1.20e-02 8.81e-03 1.23e-02 6.79e-04 0.021947 1.007 9.64e-05
## 804 2.86e-03 -8.76e-03 -1.91e-02 4.86e-03 1.95e-03 -0.043955 0.998 3.86e-04
## 805 6.12e-03 1.28e-03 4.35e-03 3.37e-03 -9.27e-03 0.012421 1.007 3.09e-05
## 806 -7.77e-03 1.22e-02 -1.90e-02 1.95e-02 1.65e-04 0.035295 1.010 2.49e-04
## 807 3.13e-02 -2.19e-02 -1.02e-02 -1.01e-02 -1.57e-02 -0.037405 1.008 2.80e-04
## 808 -1.09e-02 -1.80e-03 1.70e-02 9.81e-03 1.08e-02 0.034780 1.002 2.42e-04
## 809 -8.16e-03 1.02e-02 3.09e-03 -1.32e-03 1.86e-03 0.013577 1.008 3.69e-05
## 810 9.66e-03 7.42e-03 1.27e-02 2.05e-02 -2.40e-02 0.035015 1.007 2.45e-04
## 811 -4.44e-03 8.52e-03 -3.21e-03 -3.24e-03 -4.72e-04 -0.010733 1.009 2.31e-05
## 812 1.72e-02 -1.79e-02 2.49e-02 2.15e-02 -1.32e-02 0.054009 0.999 5.83e-04
## 813 5.57e-03 2.43e-03 -3.23e-02 2.16e-04 1.89e-03 0.038009 1.006 2.89e-04
## 814 -4.25e-02 -2.93e-02 5.14e-02 -7.25e-03 5.84e-02 -0.085641 1.007 1.47e-03
## 815 1.94e-02 5.25e-03 -2.58e-02 -2.83e-03 -1.77e-02 0.034592 1.008 2.39e-04
## 816 -1.39e-02 3.79e-02 -4.23e-02 -4.64e-04 -2.49e-04 0.062601 1.007 7.84e-04
## 817 -6.44e-02 1.47e-01 4.08e-02 6.94e-02 -6.40e-02 0.170500 0.999 5.80e-03
## 818 -1.22e-02 5.39e-02 2.10e-02 2.93e-02 -3.82e-02 0.071925 1.005 1.03e-03
## 819 -8.56e-03 2.68e-02 3.16e-02 4.60e-02 -2.67e-02 0.071963 0.998 1.03e-03
## 820 -1.73e-03 6.94e-03 5.58e-03 5.80e-03 -5.41e-03 0.013274 1.006 3.53e-05
## 821 -1.41e-02 -1.29e-02 2.73e-02 3.44e-02 1.50e-02 0.058323 1.000 6.80e-04
## 822 -9.57e-03 -1.59e-03 5.22e-03 5.46e-03 1.06e-02 0.015105 1.008 4.57e-05
## 823 -3.93e-02 -1.90e-02 3.31e-02 3.87e-02 4.77e-02 0.083389 0.997 1.39e-03
## 824 1.86e-02 2.11e-02 -2.72e-02 1.64e-02 -3.42e-02 0.052042 1.011 5.42e-04
## 825 1.51e-02 2.03e-02 1.46e-02 1.42e-02 -3.84e-02 0.048284 1.006 4.66e-04
## 826 1.53e-03 -3.72e-03 -2.20e-03 -3.52e-03 2.34e-03 -0.006004 1.008 7.22e-06
## 827 3.32e-02 -7.15e-02 2.62e-02 1.59e-02 1.25e-02 0.087512 1.000 1.53e-03
## 828 -5.78e-02 2.32e-03 2.16e-02 2.16e-02 5.82e-02 0.075655 1.005 1.14e-03
## 829 8.83e-03 -5.10e-03 1.94e-02 1.49e-02 -1.12e-02 0.039643 1.001 3.14e-04
## 830 1.58e-02 -1.09e-02 -1.92e-02 -3.96e-03 -2.53e-03 0.025162 1.009 1.27e-04
## 831 4.57e-04 -2.19e-03 -2.37e-03 -9.64e-04 1.52e-03 -0.005279 1.006 5.58e-06
## 832 7.14e-02 -1.42e-01 2.94e-02 -6.92e-03 3.15e-02 0.154485 0.998 4.76e-03
## 833 2.41e-02 -2.49e-02 -3.34e-02 -9.69e-03 5.10e-03 0.045510 1.008 4.14e-04
## 834 -5.10e-03 4.30e-02 -7.38e-02 4.07e-03 -5.63e-03 0.096835 1.000 1.87e-03
## 835 2.09e-02 3.98e-03 8.98e-03 7.30e-03 -2.99e-02 0.034528 1.008 2.39e-04
## 836 2.41e-03 2.07e-03 5.67e-03 5.72e-03 -6.36e-03 0.012538 1.006 3.15e-05
## 837 2.53e-02 -2.49e-02 1.68e-02 6.06e-03 -1.18e-02 0.045149 1.003 4.08e-04
## 838 -1.25e-02 -6.80e-03 -1.15e-02 -9.88e-03 2.32e-02 -0.031668 1.005 2.01e-04
## 839 2.21e-03 -3.31e-03 -1.75e-03 -1.69e-03 6.08e-04 -0.004754 1.007 4.52e-06
## 840 -4.04e-02 3.46e-03 2.50e-02 -2.16e-02 5.16e-02 0.083877 0.992 1.40e-03
## 841 2.76e-03 -4.37e-03 -3.12e-03 -5.41e-03 2.06e-03 -0.008016 1.008 1.29e-05
## 842 3.57e-02 -5.54e-02 -4.82e-02 -2.16e-02 2.38e-02 0.078527 1.009 1.23e-03
## 843 -1.23e-02 3.24e-02 -1.23e-02 1.73e-03 -1.19e-02 -0.041369 1.005 3.42e-04
## 844 -4.92e-03 -5.56e-02 9.66e-02 -1.30e-02 2.24e-02 -0.128335 0.993 3.29e-03
## 845 -2.80e-02 3.70e-02 5.31e-02 -2.92e-02 -6.03e-03 -0.085461 1.004 1.46e-03
## 846 -1.07e-02 5.85e-03 -3.76e-02 6.03e-03 1.83e-02 0.050810 1.006 5.17e-04
## 847 4.18e-02 1.31e-04 3.44e-02 -3.30e-03 -4.77e-02 0.089878 0.985 1.61e-03
## 848 -1.82e-03 2.43e-03 -5.79e-03 2.02e-03 1.50e-03 0.008221 1.009 1.35e-05
## 849 -2.04e-02 2.32e-02 -9.86e-03 -2.95e-03 6.41e-03 -0.032762 1.006 2.15e-04
## 850 4.27e-02 -3.07e-02 3.13e-02 3.02e-02 -3.57e-02 0.080635 0.997 1.30e-03
## 851 2.62e-03 -2.36e-03 1.63e-02 1.43e-02 -5.98e-03 0.031986 1.003 2.05e-04
## 852 -8.23e-03 1.84e-02 1.17e-02 7.79e-03 -7.55e-03 0.029319 1.004 1.72e-04
## 853 -1.03e-02 6.28e-03 -2.62e-02 -1.29e-02 1.89e-02 0.037139 1.010 2.76e-04
## 854 5.34e-03 -2.33e-03 -2.84e-02 -2.96e-03 5.55e-03 0.033203 1.007 2.21e-04
## 855 -3.64e-02 3.54e-02 -1.75e-02 7.81e-03 1.18e-02 -0.057692 1.001 6.65e-04
## 856 -2.71e-05 -9.91e-03 8.23e-03 6.20e-03 5.78e-03 0.019070 1.005 7.28e-05
## 857 7.75e-03 2.52e-03 2.76e-02 4.53e-02 -2.62e-02 0.063399 1.002 8.04e-04
## 858 -8.51e-02 2.90e-02 2.10e-02 1.80e-02 7.02e-02 0.096191 1.007 1.85e-03
## 859 6.03e-03 -5.34e-02 2.56e-02 3.43e-02 2.36e-02 0.076462 1.004 1.17e-03
## 860 -4.55e-03 3.85e-05 1.41e-02 -1.39e-03 1.13e-03 -0.016871 1.008 5.70e-05
## 861 -7.21e-03 2.10e-02 -4.27e-02 5.42e-03 3.97e-03 0.056237 1.006 6.33e-04
## 862 -2.65e-03 4.84e-03 2.31e-02 -7.55e-03 -6.13e-03 -0.030982 1.007 1.92e-04
## 863 -4.83e-03 9.64e-03 8.36e-03 7.82e-03 -4.62e-03 0.018888 1.005 7.14e-05
## 864 3.70e-03 5.78e-02 2.38e-02 2.65e-02 -5.88e-02 0.085944 1.003 1.48e-03
## 865 -1.39e-02 1.33e-02 -2.41e-02 2.15e-03 1.28e-02 0.035936 1.009 2.58e-04
## 866 -1.84e-02 1.76e-02 1.60e-02 -4.42e-03 8.94e-03 0.042783 1.001 3.66e-04
## 867 -9.17e-03 5.10e-03 6.50e-03 7.45e-03 4.15e-03 0.015092 1.006 4.56e-05
## 868 -1.40e-02 -5.96e-03 -1.62e-02 8.28e-04 2.07e-02 -0.040728 1.001 3.32e-04
## 869 2.79e-02 -5.36e-02 3.04e-02 7.29e-03 7.44e-03 0.080668 0.993 1.30e-03
## 870 1.45e-03 -1.01e-03 1.06e-03 1.38e-03 -1.36e-03 0.002856 1.008 1.63e-06
## 871 -2.15e-02 -5.69e-05 -1.08e-02 2.50e-03 2.42e-02 -0.035236 1.004 2.48e-04
## 872 -3.05e-02 1.01e-02 1.77e-02 1.93e-03 2.69e-02 0.048802 1.001 4.76e-04
## 873 -5.91e-02 5.88e-02 -6.24e-02 1.89e-02 3.71e-02 0.112935 1.005 2.55e-03
## 874 -7.71e-03 3.80e-03 4.20e-03 2.64e-03 5.08e-03 0.011088 1.006 2.46e-05
## 875 6.46e-03 -3.70e-03 -1.29e-02 -2.35e-02 3.28e-03 -0.029028 1.006 1.69e-04
## 876 -3.56e-02 3.44e-02 2.54e-02 4.37e-02 -2.92e-04 0.065609 1.003 8.61e-04
## 877 -5.84e-03 -4.01e-02 1.78e-02 8.04e-03 3.57e-02 0.059147 1.004 7.00e-04
## 878 1.41e-02 2.24e-02 -4.61e-02 3.10e-02 -2.79e-02 0.074004 1.005 1.10e-03
## 879 -1.00e-04 2.73e-04 2.11e-04 5.22e-05 -1.16e-04 0.000512 1.006 5.25e-08
## 880 4.45e-04 2.00e-02 2.06e-02 2.76e-02 -2.56e-02 0.049676 1.003 4.94e-04
## 881 5.42e-03 -1.48e-02 2.27e-02 2.17e-02 -1.88e-03 0.046631 1.000 4.35e-04
## 882 3.03e-02 -8.45e-03 1.82e-02 1.18e-02 -3.26e-02 0.050619 1.003 5.12e-04
## 883 -4.36e-02 -2.53e-02 1.63e-02 -8.64e-03 7.37e-02 0.082370 1.005 1.36e-03
## 884 2.33e-02 -2.49e-02 2.01e-02 1.90e-02 -1.38e-02 0.050267 1.003 5.05e-04
## 885 -2.74e-04 1.39e-03 -1.15e-02 3.00e-03 2.11e-03 0.014857 1.008 4.42e-05
## 886 -8.19e-03 4.30e-03 9.69e-03 -1.73e-03 6.73e-03 0.023156 1.004 1.07e-04
## 887 4.84e-02 -2.79e-02 -1.77e-02 -2.04e-02 -2.75e-02 -0.058317 1.006 6.80e-04
## 888 -2.71e-02 2.22e-02 1.58e-02 8.85e-03 1.10e-02 0.042118 1.003 3.55e-04
## 889 4.84e-02 -2.79e-02 -1.77e-02 -2.04e-02 -2.75e-02 -0.058317 1.006 6.80e-04
## 890 -9.81e-04 5.07e-03 1.87e-03 1.50e-03 -3.37e-03 0.006570 1.008 8.64e-06
## 891 3.32e-02 -7.15e-02 2.62e-02 1.59e-02 1.25e-02 0.087512 1.000 1.53e-03
## 892 2.41e-02 -2.49e-02 -3.34e-02 -9.69e-03 5.10e-03 0.045510 1.008 4.14e-04
## 893 1.23e-02 2.34e-02 3.26e-02 2.46e-02 -4.10e-02 0.075708 0.993 1.14e-03
## 894 -7.21e-03 2.10e-02 -4.27e-02 5.42e-03 3.97e-03 0.056237 1.006 6.33e-04
## 895 7.93e-03 1.05e-02 -2.44e-02 1.89e-02 -1.49e-02 0.040503 1.008 3.28e-04
## 896 -1.09e-02 2.20e-02 1.33e-02 1.31e-02 -9.10e-03 0.033894 1.005 2.30e-04
## 897 -5.67e-03 -4.46e-03 1.20e-02 -2.99e-04 1.02e-02 0.027148 1.003 1.47e-04
## 898 -8.19e-03 4.30e-03 9.69e-03 -1.73e-03 6.73e-03 0.023156 1.004 1.07e-04
## 899 -2.74e-04 1.39e-03 -1.15e-02 3.00e-03 2.11e-03 0.014857 1.008 4.42e-05
## 900 -9.09e-04 1.62e-03 3.40e-03 3.14e-03 -1.28e-03 0.006799 1.006 9.25e-06
## 901 2.33e-02 -2.49e-02 2.01e-02 1.90e-02 -1.38e-02 0.050267 1.003 5.05e-04
## 902 -4.36e-02 -2.53e-02 1.63e-02 -8.64e-03 7.37e-02 0.082370 1.005 1.36e-03
## 903 -4.04e-02 3.46e-03 2.50e-02 -2.16e-02 5.16e-02 0.083877 0.992 1.40e-03
## 904 3.03e-02 -8.45e-03 1.82e-02 1.18e-02 -3.26e-02 0.050619 1.003 5.12e-04
## 905 -1.09e-02 -1.80e-03 1.70e-02 9.81e-03 1.08e-02 0.034780 1.002 2.42e-04
## 906 -1.59e-02 1.10e-02 3.40e-02 -4.85e-03 1.10e-04 -0.043121 1.006 3.72e-04
## 907 5.42e-03 -1.48e-02 2.27e-02 2.17e-02 -1.88e-03 0.046631 1.000 4.35e-04
## 908 4.69e-03 2.81e-02 1.12e-02 6.74e-03 -2.99e-02 0.042655 1.007 3.64e-04
## 909 -1.07e-02 5.85e-03 -3.76e-02 6.03e-03 1.83e-02 0.050810 1.006 5.17e-04
## 910 4.45e-04 2.00e-02 2.06e-02 2.76e-02 -2.56e-02 0.049676 1.003 4.94e-04
## 911 -1.37e-02 2.39e-02 2.93e-02 1.44e-02 -7.75e-03 0.062393 0.993 7.77e-04
## 912 -1.00e-04 2.73e-04 2.11e-04 5.22e-05 -1.16e-04 0.000512 1.006 5.25e-08
## 913 1.14e-02 -2.12e-03 -1.74e-02 -2.36e-03 -5.44e-03 0.021026 1.008 8.85e-05
## 914 1.41e-02 2.24e-02 -4.61e-02 3.10e-02 -2.79e-02 0.074004 1.005 1.10e-03
## 915 1.98e-02 -2.87e-02 4.72e-02 6.25e-03 -1.71e-02 -0.065939 1.006 8.70e-04
## 916 -5.84e-03 -4.01e-02 1.78e-02 8.04e-03 3.57e-02 0.059147 1.004 7.00e-04
## 917 -7.34e-02 5.58e-02 -2.26e-02 1.31e-02 3.70e-02 -0.094417 0.997 1.78e-03
## 918 -1.39e-02 3.79e-02 -4.23e-02 -4.64e-04 -2.49e-04 0.062601 1.007 7.84e-04
## 919 5.14e-03 3.17e-02 2.10e-02 1.58e-02 -3.63e-02 0.058790 1.001 6.91e-04
## 920 -3.56e-02 3.44e-02 2.54e-02 4.37e-02 -2.92e-04 0.065609 1.003 8.61e-04
## 921 -1.61e-02 1.94e-02 2.13e-02 1.32e-02 -9.85e-04 0.045959 1.000 4.22e-04
## 922 1.98e-02 -4.03e-02 2.43e-02 1.11e-02 5.01e-03 0.062041 0.999 7.69e-04
## 923 9.55e-03 -5.13e-02 2.18e-02 4.78e-03 2.78e-02 0.068506 1.001 9.38e-04
## 924 -3.64e-02 3.54e-02 -1.75e-02 7.81e-03 1.18e-02 -0.057692 1.001 6.65e-04
## 925 3.24e-02 -4.62e-03 -2.22e-02 -2.23e-02 -2.67e-02 -0.053143 1.001 5.65e-04
## 926 6.46e-03 -3.70e-03 -1.29e-02 -2.35e-02 3.28e-03 -0.029028 1.006 1.69e-04
## 927 -7.71e-03 3.80e-03 4.20e-03 2.64e-03 5.08e-03 0.011088 1.006 2.46e-05
## 928 1.92e-02 -2.70e-02 4.93e-02 7.02e-03 -1.87e-02 -0.067644 1.006 9.15e-04
## 929 1.55e-02 -5.90e-02 1.93e-02 -5.70e-03 3.05e-02 0.073417 1.001 1.08e-03
## 930 -5.91e-02 5.88e-02 -6.24e-02 1.89e-02 3.71e-02 0.112935 1.005 2.55e-03
## 931 -3.05e-02 1.01e-02 1.77e-02 1.93e-03 2.69e-02 0.048802 1.001 4.76e-04
## 932 -6.84e-04 2.85e-02 -4.85e-02 2.77e-02 -1.38e-02 0.073851 1.004 1.09e-03
## 933 1.65e-02 2.96e-02 2.34e-02 1.82e-02 -4.87e-02 0.068242 1.000 9.31e-04
## 934 -2.15e-02 -5.69e-05 -1.08e-02 2.50e-03 2.42e-02 -0.035236 1.004 2.48e-04
## 935 1.02e-02 1.19e-02 -1.13e-02 -5.47e-03 -1.94e-02 -0.030302 1.005 1.84e-04
## 936 -1.23e-02 1.97e-02 -2.15e-02 2.68e-02 -1.56e-03 0.045337 1.011 4.11e-04
## 937 2.19e-03 -1.05e-03 9.70e-03 -1.65e-04 -1.67e-03 0.020607 1.004 8.50e-05
## 938 2.70e-02 -1.21e-02 -2.20e-02 -5.18e-03 -1.35e-02 0.032931 1.010 2.17e-04
## 939 -1.64e-03 2.52e-02 9.05e-03 -8.96e-04 -1.77e-02 0.034671 1.006 2.41e-04
## 940 1.45e-03 -1.01e-03 1.06e-03 1.38e-03 -1.36e-03 0.002856 1.008 1.63e-06
## 941 2.79e-02 -5.36e-02 3.04e-02 7.29e-03 7.44e-03 0.080668 0.993 1.30e-03
## 942 -4.83e-03 9.64e-03 8.36e-03 7.82e-03 -4.62e-03 0.018888 1.005 7.14e-05
## 943 -4.94e-03 -7.79e-03 -2.79e-02 -2.98e-02 2.19e-02 -0.057985 0.998 6.72e-04
## 944 -4.64e-03 -1.37e-02 1.62e-02 7.09e-03 1.38e-02 0.036160 1.002 2.62e-04
## 945 1.77e-02 -1.27e-02 5.82e-03 -2.63e-03 -9.72e-03 0.022965 1.007 1.06e-04
## 946 9.68e-04 2.58e-03 9.93e-03 1.13e-02 -6.96e-03 0.020468 1.005 8.38e-05
## 947 -7.50e-03 3.90e-03 -1.17e-02 -3.43e-03 6.80e-03 -0.024928 1.003 1.24e-04
## 948 -8.13e-03 2.84e-03 2.36e-02 -8.25e-03 1.86e-03 -0.031105 1.007 1.94e-04
## 949 7.79e-03 -1.15e-02 -2.15e-02 -9.50e-03 9.50e-03 0.027798 1.009 1.55e-04
## 950 4.57e-04 -2.19e-03 -2.37e-03 -9.64e-04 1.52e-03 -0.005279 1.006 5.58e-06
## 951 5.67e-03 1.54e-03 -4.15e-02 1.40e-02 1.73e-03 0.053930 1.005 5.82e-04
## 952 -1.40e-02 -5.96e-03 -1.62e-02 8.28e-04 2.07e-02 -0.040728 1.001 3.32e-04
## 953 -9.17e-03 5.10e-03 6.50e-03 7.45e-03 4.15e-03 0.015092 1.006 4.56e-05
## 954 -1.84e-02 1.76e-02 1.60e-02 -4.42e-03 8.94e-03 0.042783 1.001 3.66e-04
## 955 -2.59e-02 -7.65e-03 2.08e-02 7.74e-03 3.36e-02 0.053249 1.000 5.67e-04
## 956 -7.98e-03 4.20e-04 3.17e-03 4.40e-03 7.48e-03 0.010518 1.010 2.21e-05
## 957 -6.68e-04 -2.27e-03 1.23e-03 3.04e-04 2.47e-03 0.003847 1.007 2.96e-06
## 958 -1.39e-02 1.33e-02 -2.41e-02 2.15e-03 1.28e-02 0.035936 1.009 2.58e-04
## 959 -2.56e-02 7.28e-02 3.00e-02 3.23e-02 -3.85e-02 0.094860 0.998 1.80e-03
## 960 6.67e-03 -4.99e-02 -3.04e-02 -3.67e-02 4.40e-02 -0.083149 0.998 1.38e-03
## 961 3.70e-03 5.78e-02 2.38e-02 2.65e-02 -5.88e-02 0.085944 1.003 1.48e-03
## 962 5.01e-02 -2.86e-02 2.11e-02 1.85e-03 -3.64e-02 0.069016 1.000 9.52e-04
## 963 -1.73e-02 1.17e-02 -1.90e-02 1.29e-02 1.35e-02 0.035532 1.011 2.53e-04
## 964 -1.73e-03 6.94e-03 5.58e-03 5.80e-03 -5.41e-03 0.013274 1.006 3.53e-05
## 965 -2.65e-03 4.84e-03 2.31e-02 -7.55e-03 -6.13e-03 -0.030982 1.007 1.92e-04
## 966 1.19e-02 -2.57e-02 2.87e-02 1.95e-02 -1.39e-04 0.061129 0.996 7.46e-04
## 967 3.33e-02 -7.95e-03 -2.16e-02 -2.04e-02 -2.57e-02 -0.052252 1.001 5.46e-04
## 968 1.43e-03 -5.35e-04 5.72e-04 2.03e-04 -1.31e-03 0.001951 1.008 7.62e-07
## 969 -4.55e-03 3.85e-05 1.41e-02 -1.39e-03 1.13e-03 -0.016871 1.008 5.70e-05
## 970 6.03e-03 -5.34e-02 2.56e-02 3.43e-02 2.36e-02 0.076462 1.004 1.17e-03
## 971 -8.51e-02 2.90e-02 2.10e-02 1.80e-02 7.02e-02 0.096191 1.007 1.85e-03
## 972 7.75e-03 2.52e-03 2.76e-02 4.53e-02 -2.62e-02 0.063399 1.002 8.04e-04
## 973 5.52e-03 -4.82e-02 2.52e-02 9.76e-03 2.83e-02 0.070656 0.998 9.98e-04
## 974 -2.71e-05 -9.91e-03 8.23e-03 6.20e-03 5.78e-03 0.019070 1.005 7.28e-05
## 975 -3.06e-02 4.23e-04 7.47e-02 1.25e-02 8.04e-03 -0.085786 1.000 1.47e-03
## 976 5.34e-03 -2.33e-03 -2.84e-02 -2.96e-03 5.55e-03 0.033203 1.007 2.21e-04
## 977 -1.66e-03 5.65e-04 4.23e-03 -1.78e-04 1.73e-04 -0.005045 1.008 5.10e-06
## 978 -1.13e-02 4.08e-02 1.95e-02 3.11e-02 -2.95e-02 0.059772 1.006 7.15e-04
## 979 -1.03e-02 6.28e-03 -2.62e-02 -1.29e-02 1.89e-02 0.037139 1.010 2.76e-04
## 980 -8.23e-03 1.84e-02 1.17e-02 7.79e-03 -7.55e-03 0.029319 1.004 1.72e-04
## 981 6.05e-02 -2.17e-02 -5.57e-02 -2.86e-02 -2.78e-02 0.077529 1.007 1.20e-03
## 982 -5.10e-03 4.30e-02 -7.38e-02 4.07e-03 -5.63e-03 0.096835 1.000 1.87e-03
## 983 2.62e-03 -2.36e-03 1.63e-02 1.43e-02 -5.98e-03 0.031986 1.003 2.05e-04
## 984 3.83e-03 8.16e-03 5.62e-03 5.20e-03 -1.26e-02 0.017227 1.007 5.94e-05
## 985 -1.04e-02 9.23e-03 -3.46e-02 6.96e-04 1.57e-02 0.045715 1.007 4.18e-04
## 986 4.47e-04 -5.50e-03 1.33e-02 -6.84e-05 3.85e-03 0.028451 1.002 1.62e-04
## 987 3.28e-02 -2.53e-02 3.20e-02 1.37e-02 -2.29e-02 0.073694 0.992 1.08e-03
## 988 4.27e-02 -3.07e-02 3.13e-02 3.02e-02 -3.57e-02 0.080635 0.997 1.30e-03
## 989 3.71e-02 -4.64e-02 1.22e-02 -5.50e-03 -4.66e-03 0.056407 1.007 6.37e-04
## 990 4.74e-03 7.24e-03 -2.38e-02 8.90e-03 -6.04e-03 0.032090 1.007 2.06e-04
## 991 -1.41e-03 -9.35e-03 6.97e-03 -1.86e-03 7.35e-03 -0.013562 1.014 3.68e-05
## 992 -2.51e-03 1.25e-03 -1.85e-03 2.35e-04 1.85e-03 -0.004757 1.006 4.53e-06
## 993 9.66e-03 7.42e-03 1.27e-02 2.05e-02 -2.40e-02 0.035015 1.007 2.45e-04
## 994 -2.03e-02 1.76e-02 1.95e-02 -9.12e-03 1.28e-02 0.052719 0.998 5.55e-04
## 995 -1.66e-03 7.94e-03 1.10e-02 6.54e-03 -6.53e-03 0.023298 1.004 1.09e-04
## 996 -6.50e-04 8.02e-03 5.33e-03 5.95e-03 -7.57e-03 0.014130 1.007 4.00e-05
## 997 -2.04e-02 2.32e-02 -9.86e-03 -2.95e-03 6.41e-03 -0.032762 1.006 2.15e-04
## 998 -1.82e-03 2.43e-03 -5.79e-03 2.02e-03 1.50e-03 0.008221 1.009 1.35e-05
## 999 1.74e-04 3.03e-03 5.12e-03 4.50e-03 -4.11e-03 0.010794 1.006 2.33e-05
## 1000 4.18e-02 1.31e-04 3.44e-02 -3.30e-03 -4.77e-02 0.089878 0.985 1.61e-03
## 1001 -2.80e-02 3.70e-02 5.31e-02 -2.92e-02 -6.03e-03 -0.085461 1.004 1.46e-03
## 1002 -4.92e-03 -5.56e-02 9.66e-02 -1.30e-02 2.24e-02 -0.128335 0.993 3.29e-03
## 1003 -1.23e-02 3.24e-02 -1.23e-02 1.73e-03 -1.19e-02 -0.041369 1.005 3.42e-04
## 1004 -2.17e-02 1.43e-02 2.26e-02 4.34e-03 1.25e-02 0.051314 0.997 5.26e-04
## 1005 3.57e-02 -5.54e-02 -4.82e-02 -2.16e-02 2.38e-02 0.078527 1.009 1.23e-03
## 1006 2.76e-03 -4.37e-03 -3.12e-03 -5.41e-03 2.06e-03 -0.008016 1.008 1.29e-05
## 1007 2.21e-03 -3.31e-03 -1.75e-03 -1.69e-03 6.08e-04 -0.004754 1.007 4.52e-06
## 1008 1.35e-03 -3.18e-03 3.73e-03 3.07e-03 -8.95e-05 0.007899 1.006 1.25e-05
## 1009 -1.06e-02 9.25e-03 -1.46e-02 1.60e-02 5.44e-03 0.029193 1.011 1.71e-04
## 1010 9.87e-04 1.46e-04 4.82e-04 3.31e-04 -1.38e-03 0.001665 1.008 5.55e-07
## 1011 1.29e-02 -9.26e-04 -1.88e-02 -4.71e-03 -1.28e-02 -0.040066 1.000 3.21e-04
## 1012 -5.61e-02 6.77e-02 3.97e-02 5.01e-02 -5.02e-03 0.104978 0.992 2.20e-03
## 1013 2.61e-02 -2.27e-02 -4.44e-02 -4.94e-03 3.24e-03 0.056132 1.005 6.30e-04
## 1014 3.34e-02 1.05e-02 2.60e-02 2.91e-04 -5.59e-02 -0.064265 1.019 8.27e-04
## 1015 -1.25e-02 -6.80e-03 -1.15e-02 -9.88e-03 2.32e-02 -0.031668 1.005 2.01e-04
## 1016 2.53e-02 -2.49e-02 1.68e-02 6.06e-03 -1.18e-02 0.045149 1.003 4.08e-04
## 1017 1.38e-02 3.28e-02 -5.78e-02 -8.69e-03 -2.13e-02 0.074800 1.004 1.12e-03
## 1018 2.41e-03 2.07e-03 5.67e-03 5.72e-03 -6.36e-03 0.012538 1.006 3.15e-05
## 1019 2.09e-02 3.98e-03 8.98e-03 7.30e-03 -2.99e-02 0.034528 1.008 2.39e-04
## 1020 7.14e-02 -1.42e-01 2.94e-02 -6.92e-03 3.15e-02 0.154485 0.998 4.76e-03
## 1021 -1.63e-02 -2.12e-02 3.71e-02 3.10e-02 2.53e-02 0.078060 0.991 1.22e-03
## 1022 1.58e-02 -1.09e-02 -1.92e-02 -3.96e-03 -2.53e-03 0.025162 1.009 1.27e-04
## 1023 5.57e-03 2.43e-03 -3.23e-02 2.16e-04 1.89e-03 0.038009 1.006 2.89e-04
## 1024 -8.16e-03 1.02e-02 3.09e-03 -1.32e-03 1.86e-03 0.013577 1.008 3.69e-05
## 1025 7.37e-03 -4.55e-02 -2.86e-02 -3.88e-02 4.04e-02 -0.077768 1.000 1.21e-03
## 1026 -4.67e-02 6.22e-02 -1.81e-02 2.58e-03 4.40e-03 -0.075665 1.003 1.14e-03
## 1027 8.83e-03 -5.10e-03 1.94e-02 1.49e-02 -1.12e-02 0.039643 1.001 3.14e-04
## 1028 -2.44e-02 1.88e-02 2.31e-02 8.61e-03 1.07e-02 0.052343 0.998 5.48e-04
## 1029 -5.78e-02 2.32e-03 2.16e-02 2.16e-02 5.82e-02 0.075655 1.005 1.14e-03
## 1030 1.30e-02 -7.60e-03 3.19e-02 4.38e-03 -1.06e-02 0.066891 0.989 8.93e-04
## 1031 1.53e-03 -3.72e-03 -2.20e-03 -3.52e-03 2.34e-03 -0.006004 1.008 7.22e-06
## 1032 1.51e-02 2.03e-02 1.46e-02 1.42e-02 -3.84e-02 0.048284 1.006 4.66e-04
## 1033 7.38e-03 -2.35e-03 4.28e-03 3.61e-03 -7.95e-03 0.012186 1.007 2.97e-05
## 1034 2.67e-02 1.18e-03 -1.19e-02 -1.22e-02 -2.79e-02 -0.037709 1.007 2.85e-04
## 1035 4.29e-02 -3.62e-02 2.24e-02 1.84e-02 -2.76e-02 0.067505 1.002 9.11e-04
## 1036 8.31e-03 -2.01e-02 1.88e-02 2.57e-02 -2.47e-03 0.043907 1.004 3.86e-04
## 1037 1.86e-02 2.11e-02 -2.72e-02 1.64e-02 -3.42e-02 0.052042 1.011 5.42e-04
## 1038 -3.93e-02 -1.90e-02 3.31e-02 3.87e-02 4.77e-02 0.083389 0.997 1.39e-03
## 1039 -1.08e-01 4.04e-02 8.51e-02 -1.38e-02 7.05e-02 -0.139365 0.998 3.88e-03
## 1040 -3.87e-03 2.18e-02 -1.18e-02 3.74e-02 -1.91e-02 0.048703 1.021 4.75e-04
## 1041 -9.57e-03 -1.59e-03 5.22e-03 5.46e-03 1.06e-02 0.015105 1.008 4.57e-05
## 1042 9.04e-03 -5.90e-02 -2.85e-02 -2.82e-02 4.55e-02 -0.085970 0.998 1.48e-03
## 1043 2.59e-02 -4.64e-02 -1.94e-02 -3.38e-02 1.78e-02 -0.062106 1.007 7.72e-04
## 1044 -1.41e-02 -1.29e-02 2.73e-02 3.44e-02 1.50e-02 0.058323 1.000 6.80e-04
## 1045 -8.56e-03 2.68e-02 3.16e-02 4.60e-02 -2.67e-02 0.071963 0.998 1.03e-03
## 1046 -3.71e-02 2.81e-02 3.23e-02 4.20e-02 6.88e-03 0.072608 0.997 1.05e-03
## 1047 -1.22e-02 5.39e-02 2.10e-02 2.93e-02 -3.82e-02 0.071925 1.005 1.03e-03
## 1048 2.01e-02 -5.18e-03 7.31e-03 1.60e-03 -1.98e-02 0.026967 1.007 1.46e-04
## 1049 -6.44e-02 1.47e-01 4.08e-02 6.94e-02 -6.40e-02 0.170500 0.999 5.80e-03
## 1050 1.94e-02 5.25e-03 -2.58e-02 -2.83e-03 -1.77e-02 0.034592 1.008 2.39e-04
## 1051 -4.25e-02 -2.93e-02 5.14e-02 -7.25e-03 5.84e-02 -0.085641 1.007 1.47e-03
## 1052 1.72e-02 -1.79e-02 2.49e-02 2.15e-02 -1.32e-02 0.054009 0.999 5.83e-04
## 1053 -7.88e-03 1.55e-02 2.39e-02 4.76e-03 -4.62e-03 0.051278 0.996 5.25e-04
## 1054 -6.75e-03 -1.00e-02 2.20e-02 7.23e-03 1.34e-02 0.045976 0.999 4.23e-04
## 1055 4.50e-03 1.13e-03 -2.02e-02 4.94e-03 -9.99e-04 0.025313 1.007 1.28e-04
## 1056 -4.44e-03 8.52e-03 -3.21e-03 -3.24e-03 -4.72e-04 -0.010733 1.009 2.31e-05
## 1057 -3.54e-02 1.31e-02 3.61e-02 1.56e-02 1.51e-02 -0.048017 1.008 4.61e-04
## 1058 3.13e-02 -2.19e-02 -1.02e-02 -1.01e-02 -1.57e-02 -0.037405 1.008 2.80e-04
## 1059 1.38e-02 7.68e-03 -2.10e-02 -7.33e-03 -1.96e-02 -0.046156 0.999 4.26e-04
## 1060 -3.42e-03 -2.27e-05 -4.58e-03 -5.66e-04 5.63e-03 0.007853 1.012 1.23e-05
## 1061 -7.77e-03 1.22e-02 -1.90e-02 1.95e-02 1.65e-04 0.035295 1.010 2.49e-04
## 1062 -5.92e-03 5.40e-03 3.19e-03 7.63e-04 2.38e-03 0.009362 1.006 1.75e-05
## 1063 6.76e-02 -7.05e-03 -4.29e-02 -4.13e-02 -5.92e-02 -0.106869 0.987 2.28e-03
## 1064 6.12e-03 1.28e-03 4.35e-03 3.37e-03 -9.27e-03 0.012421 1.007 3.09e-05
## 1065 2.86e-03 -8.76e-03 -1.91e-02 4.86e-03 1.95e-03 -0.043955 0.998 3.86e-04
## 1066 4.00e-03 -1.20e-02 8.81e-03 1.23e-02 6.79e-04 0.021947 1.007 9.64e-05
## 1067 1.42e-04 -9.25e-04 2.68e-02 2.03e-02 -6.26e-03 0.051983 0.997 5.40e-04
## 1068 1.02e-02 -1.14e-02 1.74e-02 1.89e-02 -9.25e-03 0.037737 1.003 2.85e-04
## 1069 4.46e-04 -1.70e-03 6.42e-03 -7.42e-03 7.67e-04 -0.011959 1.010 2.86e-05
## 1070 -2.70e-03 -5.42e-02 2.25e-02 9.37e-03 4.28e-02 0.075871 1.002 1.15e-03
## 1071 -3.08e-02 -8.29e-04 9.50e-03 6.74e-03 3.42e-02 0.040289 1.010 3.25e-04
## 1072 -2.09e-02 8.55e-03 -3.71e-02 1.03e-02 2.67e-02 0.057002 1.007 6.50e-04
## 1073 -9.13e-03 4.97e-02 -1.03e-01 -2.83e-02 1.19e-02 0.129590 0.994 3.35e-03
## 1074 5.28e-02 -6.02e-02 3.53e-02 2.22e-02 -2.14e-02 0.097914 0.992 1.91e-03
## 1075 1.51e-02 -8.23e-03 -5.26e-03 -3.37e-03 -9.93e-03 -0.018320 1.008 6.72e-05
## 1076 -1.76e-01 -5.91e-02 4.92e-02 3.40e-02 2.40e-01 0.261219 0.989 1.36e-02
## 1077 -3.26e-02 4.30e-02 1.74e-02 1.69e-02 -1.63e-03 0.055699 1.004 6.21e-04
## 1078 9.01e-03 -1.07e-02 1.53e-02 -1.05e-03 -1.72e-03 0.034392 1.001 2.37e-04
## 1079 1.10e-02 1.01e-02 -2.13e-02 -2.67e-02 -1.18e-02 -0.045534 1.002 4.15e-04
## 1080 -3.94e-03 1.01e-02 -5.64e-03 -3.53e-03 -2.21e-03 -0.014822 1.006 4.40e-05
## 1081 1.29e-02 -4.12e-02 7.66e-02 -2.28e-02 -7.54e-04 -0.105913 0.998 2.24e-03
## 1082 -6.11e-03 -4.06e-02 4.20e-02 4.16e-03 2.48e-02 -0.064521 1.008 8.33e-04
## 1083 -1.84e-03 -1.54e-02 -5.94e-03 -1.02e-02 1.77e-02 -0.023970 1.012 1.15e-04
## 1084 -1.90e-02 1.29e-02 5.92e-03 2.99e-03 1.09e-02 0.023009 1.008 1.06e-04
## 1085 -3.14e-03 4.32e-03 7.48e-03 9.67e-04 -2.44e-03 -0.009741 1.009 1.90e-05
## 1086 1.48e-02 -2.66e-03 -2.31e-02 1.11e-04 -7.82e-03 0.028558 1.007 1.63e-04
## 1087 1.82e-02 -2.64e-03 -8.35e-03 -7.57e-03 -1.65e-02 -0.024688 1.007 1.22e-04
## 1088 1.20e-02 -3.70e-04 -1.40e-02 1.43e-03 -9.53e-03 0.019473 1.009 7.59e-05
## 1089 -3.66e-02 9.38e-03 -2.99e-02 1.01e-02 4.22e-02 0.062040 1.012 7.70e-04
## 1090 -3.58e-02 1.83e-03 2.07e-02 -4.58e-02 5.56e-02 0.094914 0.991 1.80e-03
## 1091 5.10e-03 -1.11e-02 1.64e-02 -6.98e-03 -4.95e-04 -0.024711 1.009 1.22e-04
## 1092 2.05e-02 -1.31e-02 8.99e-03 2.79e-03 -1.45e-02 0.028763 1.006 1.66e-04
## 1093 7.73e-04 4.73e-03 -3.50e-03 -4.47e-03 -3.13e-03 -0.008868 1.007 1.57e-05
## 1094 1.74e-03 -4.60e-03 -5.42e-03 -5.42e-03 3.42e-03 -0.011621 1.006 2.70e-05
## 1095 4.39e-03 1.09e-02 -9.81e-03 1.72e-03 -1.43e-02 -0.026348 1.004 1.39e-04
## 1096 -2.81e-03 4.24e-03 1.36e-02 1.34e-02 -4.57e-03 0.026866 1.004 1.44e-04
## 1097 -1.15e-02 1.31e-02 -3.43e-02 -1.74e-03 1.45e-02 0.045608 1.007 4.16e-04
## 1098 1.77e-02 -1.57e-02 -1.71e-02 -3.68e-03 -1.70e-03 0.025790 1.010 1.33e-04
## 1099 4.21e-02 -5.46e-02 2.20e-02 9.90e-03 -9.23e-03 0.073123 1.002 1.07e-03
## 1100 1.61e-02 -3.12e-02 1.32e-02 1.51e-03 5.40e-03 0.040869 1.004 3.34e-04
## 1101 -7.36e-02 2.83e-02 -7.53e-02 -1.65e-02 9.19e-02 0.136295 1.005 3.71e-03
## 1102 1.80e-02 2.96e-03 1.49e-02 1.04e-02 -2.68e-02 0.039156 1.004 3.07e-04
## 1103 1.16e-02 1.43e-02 1.84e-02 1.35e-03 -2.53e-02 0.047076 1.000 4.43e-04
## 1104 4.52e-02 -1.03e-02 -4.16e-02 -7.56e-03 -2.92e-02 0.059107 1.007 6.99e-04
## 1105 -2.33e-03 3.13e-03 6.05e-03 5.18e-04 -1.86e-03 -0.007758 1.009 1.20e-05
## 1106 2.75e-03 -3.00e-02 3.96e-02 -1.58e-02 1.22e-02 -0.059558 1.007 7.10e-04
## 1107 -3.94e-02 3.21e-02 4.10e-02 4.38e-02 5.83e-03 0.087860 0.989 1.54e-03
## 1108 2.39e-02 -1.38e-02 -2.21e-02 3.02e-03 -1.06e-02 0.033656 1.009 2.27e-04
## 1109 2.91e-02 9.75e-03 -3.79e-02 7.87e-03 -3.16e-02 0.055872 1.007 6.25e-04
## 1110 6.35e-02 -2.45e-02 -4.20e-02 -8.43e-03 -3.89e-02 0.071877 1.010 1.03e-03
## 1111 -1.05e-02 -6.61e-03 -4.40e-02 -5.45e-02 3.57e-02 -0.093062 0.988 1.73e-03
## 1112 2.96e-02 5.14e-02 -6.07e-02 1.59e-02 -6.02e-02 0.102177 1.005 2.09e-03
## 1113 7.25e-02 -6.73e-02 -6.23e-02 -1.55e-02 -6.84e-03 0.101436 1.006 2.06e-03
## 1114 -2.45e-03 1.02e-03 -1.30e-03 -2.97e-04 2.15e-03 -0.003749 1.007 2.81e-06
## 1115 -4.71e-02 5.70e-02 -7.96e-02 1.26e-02 3.17e-02 0.122030 0.999 2.97e-03
## 1116 -3.02e-02 -1.38e-02 -2.23e-02 -8.54e-03 4.90e-02 -0.066014 0.999 8.71e-04
## 1117 4.06e-04 1.05e-02 3.67e-03 2.30e-03 -9.50e-03 0.014507 1.009 4.21e-05
## 1118 1.58e-02 -7.27e-03 -5.32e-02 -1.61e-02 8.82e-03 0.061241 1.004 7.50e-04
## 1119 6.19e-02 1.95e-02 6.57e-02 -2.02e-02 -1.03e-01 -0.136644 1.006 3.73e-03
## 1120 -1.57e-02 6.33e-03 -7.97e-03 7.97e-03 1.06e-02 -0.026268 1.005 1.38e-04
## 1121 2.20e-03 -2.89e-02 1.99e-02 -5.32e-03 1.54e-02 -0.038452 1.013 2.96e-04
## 1122 -1.07e-02 -9.46e-03 -4.57e-02 -1.60e-02 3.90e-02 0.064461 1.007 8.31e-04
## 1123 -4.83e-03 -7.80e-03 -2.41e-02 -3.13e-02 2.23e-02 -0.052360 1.001 5.48e-04
## 1124 1.13e-02 -1.56e-02 -3.35e-02 -4.11e-02 1.30e-02 -0.068441 0.995 9.36e-04
## 1125 -3.35e-03 2.97e-03 -3.04e-03 -2.42e-03 2.37e-03 -0.007251 1.006 1.05e-05
## 1126 6.64e-03 -5.53e-03 -1.88e-02 2.01e-03 2.17e-03 0.023442 1.007 1.10e-04
## 1127 8.77e-03 -1.12e-02 8.04e-03 1.02e-02 -4.80e-03 0.021035 1.007 8.86e-05
## 1128 1.57e-03 -1.20e-03 7.20e-04 4.62e-04 -1.04e-03 0.002285 1.008 1.04e-06
## 1129 -1.26e-04 1.28e-04 1.67e-04 -5.41e-05 6.56e-06 -0.000257 1.010 1.33e-08
## 1130 9.19e-03 -5.41e-03 -2.08e-02 2.30e-03 -3.38e-04 0.025819 1.007 1.33e-04
## 1131 -8.86e-03 1.32e-02 1.02e-02 6.73e-03 -2.39e-03 0.023907 1.005 1.14e-04
## 1132 -4.20e-02 -4.71e-02 1.04e-01 3.19e-02 4.45e-02 -0.132596 0.994 3.51e-03
## 1133 2.45e-02 -1.20e-01 -4.52e-02 -4.12e-02 8.00e-02 -0.156118 0.983 4.85e-03
## 1134 2.19e-02 2.44e-02 1.61e-02 1.52e-02 -4.99e-02 0.059441 1.006 7.07e-04
## 1135 -3.80e-02 1.42e-02 -2.80e-02 -3.35e-02 4.43e-02 -0.074438 1.000 1.11e-03
## 1136 1.15e-02 -2.99e-03 2.07e-02 6.02e-03 -1.31e-02 0.043824 0.999 3.84e-04
## 1137 -3.86e-03 1.25e-02 7.20e-03 2.40e-03 -6.16e-03 0.019452 1.005 7.57e-05
## 1138 -7.46e-03 -8.05e-03 -6.62e-03 -2.28e-03 1.58e-02 -0.021116 1.006 8.92e-05
## 1139 2.82e-02 -9.88e-03 -2.08e-02 -5.08e-03 -2.34e-02 -0.050950 0.999 5.19e-04
## 1140 1.78e-02 -4.08e-02 -2.24e-02 -2.51e-02 1.99e-02 -0.060223 1.002 7.25e-04
## 1141 4.53e-03 -2.56e-04 -7.84e-03 2.54e-03 -3.25e-03 0.010607 1.008 2.25e-05
## 1142 3.31e-02 -3.05e-02 2.75e-02 3.83e-02 -2.74e-02 0.072688 1.002 1.06e-03
## 1143 3.22e-02 -2.20e-02 -3.60e-02 -8.10e-03 -6.30e-03 0.048368 1.007 4.68e-04
## 1144 7.11e-03 1.66e-02 -1.59e-02 2.14e-04 -1.65e-02 0.027760 1.012 1.54e-04
## 1145 8.45e-03 -2.33e-02 1.86e-02 3.86e-03 1.65e-03 -0.031702 1.012 2.01e-04
## 1146 -4.70e-02 3.77e-02 1.59e-02 1.14e-02 2.12e-02 0.058831 1.005 6.92e-04
## 1147 -9.95e-05 2.30e-03 2.99e-03 3.13e-03 -2.75e-03 0.006568 1.006 8.63e-06
## 1148 -1.63e-02 9.01e-03 1.89e-02 5.07e-04 5.70e-03 -0.025288 1.008 1.28e-04
## 1149 -3.66e-04 3.14e-03 -1.01e-02 4.58e-03 -5.83e-05 0.014017 1.008 3.93e-05
## 1150 -1.88e-02 1.76e-02 -6.94e-02 -5.72e-03 3.17e-02 0.090002 1.001 1.62e-03
## 1151 2.34e-02 -2.33e-02 1.61e-02 7.31e-03 -1.13e-02 0.042722 1.003 3.65e-04
## 1152 2.24e-03 -2.99e-03 -2.04e-03 1.36e-03 -7.09e-04 -0.006179 1.006 7.64e-06
## 1153 -7.12e-03 4.74e-02 -2.92e-02 -3.93e-02 -1.59e-02 -0.077000 1.001 1.19e-03
## 1154 4.91e-03 -2.85e-03 1.19e-02 1.42e-03 -3.94e-03 0.024957 1.003 1.25e-04
## 1155 -7.04e-05 4.98e-04 4.29e-04 2.03e-04 -3.80e-04 0.001015 1.006 2.06e-07
## 1156 -2.57e-03 -7.03e-02 2.26e-02 2.31e-04 5.84e-02 0.093309 1.002 1.74e-03
## 1157 2.30e-03 -4.01e-03 1.58e-03 -8.41e-04 7.72e-04 0.005394 1.007 5.82e-06
## 1158 -6.69e-03 6.67e-03 5.38e-03 8.91e-04 2.22e-03 0.013636 1.005 3.72e-05
## 1159 -2.71e-02 1.50e-02 9.09e-03 3.35e-03 1.86e-02 0.033334 1.007 2.22e-04
## 1160 5.86e-03 3.42e-02 -2.95e-02 -3.90e-02 -2.07e-02 -0.071130 1.000 1.01e-03
## 1161 -1.67e-03 -6.57e-03 5.91e-03 2.22e-03 4.69e-03 -0.010012 1.014 2.01e-05
## 1162 -1.34e-02 2.08e-02 2.08e-02 3.18e-03 -1.89e-03 0.048089 0.998 4.62e-04
## 1163 -7.09e-02 2.08e-02 2.04e-02 4.37e-03 6.47e-02 0.086500 1.003 1.50e-03
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## 992 0.00157
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## 1166 0.00234
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## 1185 0.00378
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## 1188 0.00159
## 1189 0.00373
## 1190 0.00415
plot(fit)
# Assessing Outliers
library(car)
outlierTest(fit)
## No Studentized residuals with Bonferroni p < 0.05
## Largest |rstudent|:
## rstudent unadjusted p-value Bonferroni p
## 498 -3.402308 0.00069051 0.8217
leveragePlots(fit) # leverage plots
# Influential Observations
# added variable plots
avPlots(fit)
# Cook's D plot
# identify D values > 4/(n-k-1)
cutoff <- 4/((nrow(heart)-length(fit$coefficients)-2))
plot(fit, which=4, cook.levels=cutoff)
# Influence Plot
influencePlot(fit, id.method="identify", main="Influence Plot", sub="Circle size is proportial to Cook's Distance" )
## Warning in plot.window(...): "id.method" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "id.method" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "id.method" is not
## a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "id.method" is not
## a graphical parameter
## Warning in box(...): "id.method" is not a graphical parameter
## Warning in title(...): "id.method" is not a graphical parameter
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "id.method" is not a
## graphical parameter
## StudRes Hat CookD
## 367 0.7633168 0.021967548 0.002618309
## 401 -2.1027738 0.017486732 0.015693981
## 451 1.0341150 0.049232447 0.011074377
## 498 -3.4023085 0.007276853 0.016820314
## 509 -3.2412109 0.004097064 0.008574930
# Normality of Residuals
# qq plot for studentized resid
qqPlot(fit, main="QQ Plot")
## [1] 498 509
# distribution of studentized residuals
library(MASS)
sresid <- studres(fit)
hist(sresid, freq=FALSE,
main="Distribution of Studentized Residuals")
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
#Non-constant Error Variance
# Evaluate homoscedasticity
# non-constant error variance test
ncvTest(fit)
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.001051801, Df = 1, p = 0.97413
# plot studentized residuals vs. fitted values
spreadLevelPlot(fit)
##
## Suggested power transformation: 0.6708882
#Multi-collinearity
# Evaluate Collinearity
vif(fit) # variance inflation factors
## age sex cholesterol resting.bp.s
## 1.077171 1.045647 1.061595 1.085690
sqrt(vif(fit)) > 2 # problem?
## age sex cholesterol resting.bp.s
## FALSE FALSE FALSE FALSE
#Nonlinearity
# component + residual plot
crPlots(fit)
#Non-independence of Errors
# Test for Autocorrelated Errors
durbinWatsonTest(fit)
## lag Autocorrelation D-W Statistic p-value
## 1 0.1516354 1.695427 0
## Alternative hypothesis: rho != 0
Logistic Regression
names(heart)
## [1] "age" "sex" "chest.pain.type"
## [4] "resting.bp.s" "cholesterol" "fasting.blood.sugar"
## [7] "resting.ecg" "max.heart.rate" "exercise.angina"
## [10] "oldpeak" "ST.slope" "target"
model <- glm(target ~ age + sex + chest.pain.type + resting.bp.s + cholesterol + fasting.blood.sugar + max.heart.rate + exercise.angina + oldpeak + ST.slope, family = binomial(), data = heart)
# Summary of the model to see results
summary(model)
##
## Call:
## glm(formula = target ~ age + sex + chest.pain.type + resting.bp.s +
## cholesterol + fasting.blood.sugar + max.heart.rate + exercise.angina +
## oldpeak + ST.slope, family = binomial(), data = heart)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.4237018 1.1994085 -5.356 8.52e-08 ***
## age 0.0206234 0.0100545 2.051 0.040252 *
## sex 1.4284886 0.2117433 6.746 1.52e-11 ***
## chest.pain.type 0.7896806 0.0956835 8.253 < 2e-16 ***
## resting.bp.s 0.0069871 0.0048072 1.453 0.146100
## cholesterol -0.0022932 0.0009257 -2.477 0.013242 *
## fasting.blood.sugar 0.8250123 0.2201640 3.747 0.000179 ***
## max.heart.rate -0.0106939 0.0038852 -2.752 0.005914 **
## exercise.angina 1.0238022 0.1912930 5.352 8.70e-08 ***
## oldpeak 0.3806482 0.0952424 3.997 6.43e-05 ***
## ST.slope 1.2428213 0.1669008 7.446 9.59e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1645.80 on 1189 degrees of freedom
## Residual deviance: 922.35 on 1179 degrees of freedom
## AIC: 944.35
##
## Number of Fisher Scoring iterations: 5
# Diagnostic plots
par(mfrow = c(2, 2))
plot(model)
# Predicting probabilities
predicted_probabilities <- predict(model, type = "response")
# Converting probabilities to binary outcome based on a 0.5 cutoff
predicted_classes <- ifelse(predicted_probabilities > 0.5, 1, 0)
# Creating a confusion matrix to see the accuracy
table(Predicted = predicted_classes, Actual = heart$target)
## Actual
## Predicted 0 1
## 0 465 103
## 1 96 526
Inference:
Linear Discriminant Analysis
library(MASS)
heart$target <- factor(heart$target)
# Apply LDA
heart_lda <- lda(target ~ age + sex + chest.pain.type + resting.bp.s + cholesterol +
fasting.blood.sugar + resting.ecg + max.heart.rate + exercise.angina +
oldpeak + ST.slope, data = heart)
# Summary of the LDA model
summary(heart_lda)
## Length Class Mode
## prior 2 -none- numeric
## counts 2 -none- numeric
## means 22 -none- numeric
## scaling 11 -none- numeric
## lev 2 -none- character
## svd 1 -none- numeric
## N 1 -none- numeric
## call 3 -none- call
## terms 3 terms call
## xlevels 0 -none- list
# Plotting the LDA model
plot(heart_lda)
# Optionally, predicting and evaluating the model
heart_predictions <- predict(heart_lda)
table(predicted = heart_predictions$class, actual = heart$target)
## actual
## predicted 0 1
## 0 463 102
## 1 98 527
Inference:
Conclusion:
The analysis emphasizes the importance of several key risk factors, including age, sex, blood pressure, cholesterol, and specific symptoms like chest pain type and exercise-induced angina. These findings can inform public health policies and patient education programs focusing on these risk factors.
In summary, this dataset analysis not only provides insights into the epidemiological factors of heart disease but also showcases how various statistical and machine learning techniques can be effectively used to uncover patterns, predict outcomes, and potentially guide clinical decisions. This kind of multidimensional analysis is crucial in advancing healthcare towards more personalized and preemptive strategies.